{"id":300589,"date":"2023-12-29T16:25:35","date_gmt":"2023-12-29T09:25:35","guid":{"rendered":"https:\/\/hoanghamobile.com\/tin-tuc\/?p=300589"},"modified":"2025-12-16T23:32:31","modified_gmt":"2025-12-16T16:32:31","slug":"dien-tich-tam-giac","status":"publish","type":"post","link":"https:\/\/hoanghamobile.com\/tin-tuc\/dien-tich-tam-giac\/","title":{"rendered":"C\u00e1c c\u00f4ng th\u1ee9c t\u00ednh di\u1ec7n t\u00edch tam gi\u00e1c \u0111\u1ea7y \u0111\u1ee7 chi ti\u1ebft nh\u1ea5t 2025"},"content":{"rendered":"<p><span style=\"font-weight: 400;\">Trong h\u00ecnh h\u1ecdc l\u1edbp 5-12, c\u00e1c c\u00f4ng th\u1ee9c t\u00ednh di\u1ec7n t\u00edch tam gi\u00e1c l\u00e0 ki\u1ebfn th\u1ee9c c\u01a1 b\u1ea3n, gi\u00fap gi\u1ea3i quy\u1ebft nhanh b\u00e0i t\u1eadp v\u00e0 \u1ee9ng d\u1ee5ng th\u1ef1c t\u1ebf nh\u01b0 ki\u1ebfn tr\u00fac, \u0111o l\u01b0\u1eddng. B\u00e0i vi\u1ebft t\u1ed5ng h\u1ee3p \u0111\u1ea7y \u0111\u1ee7 c\u00e1c c\u00f4ng th\u1ee9c t\u00ednh di\u1ec7n t\u00edch tam gi\u00e1c chi ti\u1ebft 2025: tam gi\u00e1c th\u01b0\u1eddng, vu\u00f4ng, c\u00e2n, \u0111\u1ec1u, Heron (\u221a[p(p-a)(p-b)(p-c)]), Sin C (\u00bdab sin C), b\u00e1n k\u00ednh R\/r, t\u1ecda \u0111\u1ed9 Oxyz. K\u00e8m v\u00ed d\u1ee5 minh h\u1ecda, b\u00e0i t\u1eadp t\u1ef1 luy\u1ec7n c\u00f3 \u0111\u00e1p \u00e1n gi\u00fap h\u1ecdc sinh d\u1ec5 hi\u1ec3u v\u00e0 \u00e1p d\u1ee5ng.<\/span><\/p>\n<h2><span style=\"font-weight: 400;\">T\u00ecm hi\u1ec3u v\u1ec1 di\u1ec7n t\u00edch c\u1ee7a tam gi\u00e1c v\u00e0 \u1ee9ng d\u1ee5ng<\/span><\/h2>\n<p><span style=\"font-weight: 400;\">T\u00ednh di\u1ec7n t\u00edch kh\u00f4ng ch\u1ec9 \u0111\u01a1n thu\u1ea7n l\u00e0 m\u1ed9t ph\u00e9p t\u00ednh to\u00e1n h\u00ecnh h\u1ecdc m\u00e0 c\u00f2n l\u00e0 kh\u00e1i ni\u1ec7m c\u1ef1c k\u1ef3 quan tr\u1ecdng trong to\u00e1n h\u1ecdc v\u00e0 th\u1eadm ch\u00ed c\u1ea3 trong th\u1ef1c t\u1ebf.<\/span><\/p>\n<h3><span style=\"font-weight: 400;\">T\u1ea7m quan tr\u1ecdng<\/span><\/h3>\n<p><span style=\"font-weight: 400;\">T\u00ednh di\u1ec7n t\u00edch ch\u00ednh l\u00e0 \u0111o l\u01b0\u1eddng kh\u00f4ng gian m\u00e0 tam gi\u00e1c chi\u1ebfm tr\u00ean m\u1ed9t m\u1eb7t ph\u1eb3ng. N\u00f3 c\u00f2n \u0111\u00f3ng vai tr\u00f2 quan tr\u1ecdng trong vi\u1ec7c gi\u00fap b\u1ea1n hi\u1ec3u r\u00f5 h\u01a1n v\u1ec1 c\u00e1c \u0111\u1ecbnh l\u00fd h\u00ecnh h\u1ecdc c\u0169ng nh\u01b0 \u00e1p d\u1ee5ng ch\u00fang v\u00e0o c\u00e1c b\u00e0i to\u00e1n th\u1ef1c t\u1ebf. \u0110\u1ed3ng th\u1eddi, di\u1ec7n t\u00edch n\u00e0y c\u0169ng l\u00e0 n\u1ec1n t\u1ea3ng \u0111\u1ec3 kh\u00e1m ph\u00e1 v\u00e0 \u00e1p d\u1ee5ng c\u00e1c c\u00f4ng th\u1ee9c li\u00ean quan \u0111\u1ebfn \u0111\u01b0\u1eddng cao, \u0111\u01b0\u1eddng trung tuy\u1ebfn, v\u00e0 c\u00e1c y\u1ebfu t\u1ed1 kh\u00e1c c\u1ee7a tam gi\u00e1c.<\/span><\/p>\n<p><picture><source srcset=\"https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/webp-express\/webp-images\/uploads\/2023\/12\/dien-tich-tam-giac-1.jpg.webp 800w, https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/webp-express\/webp-images\/uploads\/2023\/12\/dien-tich-tam-giac-1-300x169.jpg.webp 300w, https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/webp-express\/webp-images\/uploads\/2023\/12\/dien-tich-tam-giac-1-768x432.jpg.webp 768w\" sizes=\"(max-width: 800px) 100vw, 800px\" type=\"image\/webp\"><img fetchpriority=\"high\" decoding=\"async\" class=\"aligncenter wp-image-300590 size-full webpexpress-processed\" src=\"https:\\\/\\\/hoanghamobile.com\/tin-tuc\/wp-content\/uploads\/2023\/12\/dien-tich-tam-giac-1.jpg\" alt=\"dien-tich-tam-giac-1\" width=\"800\" height=\"450\" srcset=\"https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/uploads\/2023\/12\/dien-tich-tam-giac-1.jpg 800w, https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/uploads\/2023\/12\/dien-tich-tam-giac-1-300x169.jpg 300w, https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/uploads\/2023\/12\/dien-tich-tam-giac-1-768x432.jpg 768w\" sizes=\"(max-width: 800px) 100vw, 800px\"><\/picture><\/p>\n<h3><span style=\"font-weight: 400;\">\u00c1p d\u1ee5ng c\u00f4ng th\u1ee9c ch\u00ednh x\u00e1c<\/span><\/h3>\n<p><span style=\"font-weight: 400;\">\u0110\u1ed1i v\u1edbi vi\u1ec7c t\u00ednh to\u00e1n <\/span><b>di\u1ec7n t\u00edch tam gi\u00e1c<\/b><span style=\"font-weight: 400;\">, s\u1ef1 ch\u00ednh x\u00e1c l\u00e0 y\u1ebfu t\u1ed1 v\u00f4 c\u00f9ng quan tr\u1ecdng. B\u1edfi c\u00f4ng th\u1ee9c t\u00ednh di\u1ec7n t\u00edch n\u00e0y kh\u00f4ng ch\u1ec9 gi\u00fap ch\u00fang ta \u0111o l\u01b0\u1eddng di\u1ec7n t\u00edch m\u1ed9t c\u00e1ch nhanh ch\u00f3ng m\u00e0 c\u00f2n \u0111\u1ea3m b\u1ea3o cho ra \u0111\u01b0\u1ee3c k\u1ebft qu\u1ea3 \u0111\u00fang. V\u00e0 ch\u1ec9 m\u1ed9t sai s\u1ed1 nh\u1ecf trong t\u00ednh to\u00e1n c\u00f3 th\u1ec3 d\u1eabn \u0111\u1ebfn k\u1ebft qu\u1ea3 ho\u00e0n to\u00e0n kh\u00e1c nhau v\u00e0 \u1ea3nh h\u01b0\u1edfng \u0111\u1ebfn qu\u00e1 tr\u00ecnh gi\u1ea3i quy\u1ebft v\u1ea5n \u0111\u1ec1 c\u0169ng nh\u01b0 \u0111i\u1ec3m s\u1ed1 c\u1ee7a b\u1ea1n.<\/span><\/p>\n<p><picture><source srcset=\"https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/webp-express\/webp-images\/uploads\/2023\/12\/dien-tich-tam-giac-2.jpg.webp 800w, https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/webp-express\/webp-images\/uploads\/2023\/12\/dien-tich-tam-giac-2-300x169.jpg.webp 300w, https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/webp-express\/webp-images\/uploads\/2023\/12\/dien-tich-tam-giac-2-768x432.jpg.webp 768w\" sizes=\"(max-width: 800px) 100vw, 800px\" type=\"image\/webp\"><img decoding=\"async\" class=\"aligncenter wp-image-300591 size-full webpexpress-processed\" src=\"https:\\\/\\\/hoanghamobile.com\/tin-tuc\/wp-content\/uploads\/2023\/12\/dien-tich-tam-giac-2.jpg\" alt=\"dien-tich-tam-giac-2\" width=\"800\" height=\"450\" srcset=\"https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/uploads\/2023\/12\/dien-tich-tam-giac-2.jpg 800w, https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/uploads\/2023\/12\/dien-tich-tam-giac-2-300x169.jpg 300w, https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/uploads\/2023\/12\/dien-tich-tam-giac-2-768x432.jpg 768w\" sizes=\"(max-width: 800px) 100vw, 800px\"><\/picture><\/p>\n<h3><span style=\"font-weight: 400;\">\u1ee8ng d\u1ee5ng th\u1ef1c t\u1ebf<\/span><\/h3>\n<p><span style=\"font-weight: 400;\">Vi\u1ec7c t\u00ednh to\u00e1n <\/span><b>di\u1ec7n t\u00edch tam gi\u00e1c<\/b><span style=\"font-weight: 400;\"> kh\u00f4ng ch\u1ec9 \u0111\u00f3ng vai tr\u00f2 trong l\u0129nh v\u1ef1c to\u00e1n h\u1ecdc m\u00e0 c\u00f2n c\u00f3 \u1ee9ng d\u1ee5ng r\u1ed9ng r\u00e3i trong th\u1ef1c t\u1ebf. Trong ki\u1ebfn tr\u00fac, x\u00e2y d\u1ef1ng, hay th\u1eadm ch\u00ed l\u00e0 trong \u0111\u1ecba l\u00fd, vi\u1ec7c t\u00ednh to\u00e1n di\u1ec7n t\u00edch n\u00e0y l\u00e0 y\u1ebfu t\u1ed1 quy\u1ebft \u0111\u1ecbnh \u0111\u1ebfn k\u1ebft qu\u1ea3 cu\u1ed1i c\u00f9ng c\u1ee7a m\u1ed9t c\u00f4ng tr\u00ecnh, m\u1ed9t thi\u1ebft k\u1ebf hay th\u1eadm ch\u00ed l\u00e0 vi\u1ec7c x\u00e1c \u0111\u1ecbnh di\u1ec7n t\u00edch \u0111\u1ea5t \u0111ai.<\/span><\/p>\n<p><picture><source srcset=\"https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/webp-express\/webp-images\/uploads\/2023\/12\/dien-tich-tam-giac-3.jpg.webp 800w, https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/webp-express\/webp-images\/uploads\/2023\/12\/dien-tich-tam-giac-3-300x169.jpg.webp 300w, https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/webp-express\/webp-images\/uploads\/2023\/12\/dien-tich-tam-giac-3-768x432.jpg.webp 768w\" sizes=\"(max-width: 800px) 100vw, 800px\" type=\"image\/webp\"><img decoding=\"async\" class=\"aligncenter wp-image-300592 size-full webpexpress-processed\" src=\"https:\\\/\\\/hoanghamobile.com\/tin-tuc\/wp-content\/uploads\/2023\/12\/dien-tich-tam-giac-3.jpg\" alt=\"dien-tich-tam-giac-3\" width=\"800\" height=\"450\" srcset=\"https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/uploads\/2023\/12\/dien-tich-tam-giac-3.jpg 800w, https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/uploads\/2023\/12\/dien-tich-tam-giac-3-300x169.jpg 300w, https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/uploads\/2023\/12\/dien-tich-tam-giac-3-768x432.jpg 768w\" sizes=\"(max-width: 800px) 100vw, 800px\"><\/picture><\/p>\n<h2><span style=\"font-weight: 400;\">Ph\u00e2n lo\u1ea1i c\u00e1c d\u1ea1ng tam gi\u00e1c th\u01b0\u1eddng g\u1eb7p<\/span><\/h2>\n<p><span style=\"font-weight: 400;\">C\u00f3 ba lo\u1ea1i ph\u00e2n lo\u1ea1i ch\u00ednh c\u1ee7a tam gi\u00e1c d\u1ef1a tr\u00ean c\u00e1c \u0111\u1eb7c t\u00ednh ri\u00eang bi\u1ec7t c\u1ee7a n\u00f3: theo c\u1ea1nh, theo g\u00f3c v\u00e0 theo \u0111\u1ed9 d\u00e0i c\u00e1c c\u1ea1nh.<\/span><\/p>\n<p><span style=\"font-weight: 400;\">\u0110\u1ea7u ti\u00ean l\u00e0 ph\u00e2n lo\u1ea1i tam gi\u00e1c theo c\u1ea1nh.\u00a0<\/span><\/p>\n<ul>\n<li style=\"font-weight: 400;\"><span style=\"font-weight: 400;\">Tam gi\u00e1c \u0111\u1ec1u \u0111\u01b0\u1ee3c x\u00e1c \u0111\u1ecbnh b\u1edfi ba c\u1ea1nh b\u1eb1ng nhau v\u00e0 ba g\u00f3c \u0111\u1ec1u c\u00f3 gi\u00e1 tr\u1ecb 60 \u0111\u1ed9.\u00a0<\/span><\/li>\n<li style=\"font-weight: 400;\"><span style=\"font-weight: 400;\">Tam gi\u00e1c c\u00e2n c\u00f3 \u00edt nh\u1ea5t hai c\u1ea1nh b\u1eb1ng nhau, t\u1ea1o ra m\u1ed9t s\u1ef1 c\u00e2n \u0111\u1ed1i t\u01b0\u01a1ng \u0111\u1ed1i.\u00a0<\/span><\/li>\n<li style=\"font-weight: 400;\"><span style=\"font-weight: 400;\">Tam gi\u00e1c vu\u00f4ng c\u00f3 m\u1ed9t g\u00f3c vu\u00f4ng \u1edf m\u1ed9t trong ba g\u00f3c c\u1ee7a n\u00f3, t\u1ee9c l\u00e0 90 \u0111\u1ed9.<\/span><\/li>\n<\/ul>\n<p><span style=\"font-weight: 400;\">Ti\u1ebfp theo l\u00e0 ph\u00e2n lo\u1ea1i tam gi\u00e1c theo g\u00f3c.\u00a0<\/span><\/p>\n<ul>\n<li style=\"font-weight: 400;\"><span style=\"font-weight: 400;\">Tam gi\u00e1c nh\u1ecdn c\u00f3 ba g\u00f3c nh\u1ecdn, m\u1ed7i g\u00f3c \u0111\u1ec1u nh\u1ecf h\u01a1n 90 \u0111\u1ed9, t\u1ea1o ra h\u00ecnh d\u00e1ng m\u1ea3nh mai v\u00e0 s\u1eafc n\u00e9t.\u00a0<\/span><\/li>\n<li style=\"font-weight: 400;\"><span style=\"font-weight: 400;\">Tam gi\u00e1c t\u00f9 c\u00f3 m\u1ed9t g\u00f3c t\u00f9, c\u00f3 m\u1ed9t g\u00f3c l\u1edbn h\u01a1n 90 \u0111\u1ed9, t\u1ea1o n\u00ean h\u00ecnh d\u00e1ng c\u00f3 \u0111\u1eb7c \u0111i\u1ec3m c\u1ea1nh b\u00ean d\u00e0i v\u00e0 g\u00f3c r\u1ed9ng.<\/span><\/li>\n<\/ul>\n<p><picture><source srcset=\"https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/webp-express\/webp-images\/uploads\/2023\/12\/dien-tich-tam-giac-4.jpg.webp 800w, https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/webp-express\/webp-images\/uploads\/2023\/12\/dien-tich-tam-giac-4-300x169.jpg.webp 300w, https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/webp-express\/webp-images\/uploads\/2023\/12\/dien-tich-tam-giac-4-768x432.jpg.webp 768w\" sizes=\"(max-width: 800px) 100vw, 800px\" type=\"image\/webp\"><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter wp-image-300593 size-full webpexpress-processed\" src=\"https:\\\/\\\/hoanghamobile.com\/tin-tuc\/wp-content\/uploads\/2023\/12\/dien-tich-tam-giac-4.jpg\" alt=\"dien-tich-tam-giac-4\" width=\"800\" height=\"450\" srcset=\"https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/uploads\/2023\/12\/dien-tich-tam-giac-4.jpg 800w, https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/uploads\/2023\/12\/dien-tich-tam-giac-4-300x169.jpg 300w, https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/uploads\/2023\/12\/dien-tich-tam-giac-4-768x432.jpg 768w\" sizes=\"(max-width: 800px) 100vw, 800px\"><\/picture><\/p>\n<p><span style=\"font-weight: 400;\">Ph\u00e2n lo\u1ea1i theo \u0111\u1ed9 d\u00e0i c\u00e1c c\u1ea1nh.<\/span><\/p>\n<ul>\n<li style=\"font-weight: 400;\"><span style=\"font-weight: 400;\">Tam gi\u00e1c th\u01b0\u1eddng kh\u00f4ng c\u00f3 \u0111\u1eb7c \u0111i\u1ec3m \u0111\u1eb7c tr\u01b0ng n\u00e0o v\u1ec1 c\u1ea1nh v\u00e0 g\u00f3c, ba c\u1ea1nh v\u00e0 ba g\u00f3c \u0111\u1ec1u kh\u00f4ng b\u1eb1ng nhau.\u00a0<\/span><\/li>\n<li style=\"font-weight: 400;\"><span style=\"font-weight: 400;\">C\u00f2n l\u1ea1i c\u00e1c lo\u1ea1i tam gi\u00e1c kh\u00e1c nh\u01b0 tam gi\u00e1c \u0111\u1ec1u, c\u00e2n, vu\u00f4ng hay t\u00f9.<\/span><\/li>\n<\/ul>\n<h2><b>T\u1ed5ng h\u1ee3p 8 c\u00f4ng th\u1ee9c t\u00ednh di\u1ec7n t\u00edch tam gi\u00e1c \u0111\u1ea7y \u0111\u1ee7 (C\u1eadp nh\u1eadt 2025)<\/b><\/h2>\n<ol>\n<li style=\"font-weight: 400;\" aria-level=\"1\"><b>C\u00f4ng th\u1ee9c c\u01a1 b\u1ea3n (\u0111\u00e1y a, cao h):<\/b><span style=\"font-weight: 400;\"> S = \u00bd \u00d7 a \u00d7 h<\/span><span style=\"font-weight: 400;\"><br \/>\n<\/span><span style=\"font-weight: 400;\">V\u00ed d\u1ee5: \u0110\u00e1y 10cm, cao 6cm \u2192 S = \u00bd \u00d7 10 \u00d7 6 = 30cm\u00b2.<\/span><\/li>\n<li style=\"font-weight: 400;\" aria-level=\"1\"><b>Tam gi\u00e1c vu\u00f4ng (c\u1ea1nh g\u00f3c vu\u00f4ng a, b):<\/b><span style=\"font-weight: 400;\"> S = \u00bd \u00d7 a \u00d7 b<\/span><span style=\"font-weight: 400;\"><br \/>\n<\/span><span style=\"font-weight: 400;\">V\u00ed d\u1ee5: a=3cm, b=4cm \u2192 S=6cm\u00b2.<\/span><\/li>\n<li style=\"font-weight: 400;\" aria-level=\"1\"><b>Tam gi\u00e1c c\u00e2n (\u0111\u00e1y a, cao h):<\/b><span style=\"font-weight: 400;\"> S = \u00bd \u00d7 a \u00d7 h (h chia \u0111\u00f4i \u0111\u00e1y).<\/span><\/li>\n<li style=\"font-weight: 400;\" aria-level=\"1\"><b>Tam gi\u00e1c \u0111\u1ec1u (c\u1ea1nh a):<\/b><span style=\"font-weight: 400;\"> S = (a\u00b2 \u00d7 \u221a3)\/4<\/span><span style=\"font-weight: 400;\"><br \/>\n<\/span><span style=\"font-weight: 400;\">V\u00ed d\u1ee5: a=6cm \u2192 S \u2248 15.59cm\u00b2.<\/span><\/li>\n<li style=\"font-weight: 400;\" aria-level=\"1\"><b>C\u00f4ng th\u1ee9c Heron (3 c\u1ea1nh a,b,c; p=(a+b+c)\/2):<\/b><span style=\"font-weight: 400;\"> S = \u221a[p(p-a)(p-b)(p-c)]<\/span><span style=\"font-weight: 400;\"><br \/>\n<\/span><span style=\"font-weight: 400;\">V\u00ed d\u1ee5: a=3, b=4, c=5; p=6 \u2192 S=\u221a[6(3)(2)(1)]=6cm\u00b2.<\/span><\/li>\n<li style=\"font-weight: 400;\" aria-level=\"1\"><b>Sin C (2 c\u1ea1nh a,b k\u1ec1 g\u00f3c C):<\/b><span style=\"font-weight: 400;\"> S = \u00bd \u00d7 a \u00d7 b \u00d7 sin C.<\/span><\/li>\n<li style=\"font-weight: 400;\" aria-level=\"1\"><b>B\u00e1n k\u00ednh ngo\u1ea1i ti\u1ebfp R:<\/b><span style=\"font-weight: 400;\"> S = abc \/ (4R).<\/span><\/li>\n<li style=\"font-weight: 400;\" aria-level=\"1\"><b>T\u1ecda \u0111\u1ed9 Oxyz (A(x1,y1,z1), B(x2,y2,z2), C(x3,y3,z3)):<\/b><span style=\"font-weight: 400;\"> S = \u00bd |AB \u00d7 AC| (t\u00edch c\u00f3 h\u01b0\u1edbng vector).<\/span><\/li>\n<\/ol>\n<h3><span style=\"font-weight: 400;\">Tam gi\u00e1c th\u01b0\u1eddng<\/span><\/h3>\n<p><span style=\"font-weight: 400;\">Tam gi\u00e1c th\u01b0\u1eddng c\u00f3 h\u00ecnh d\u00e1ng r\u1ea5t \u0111a d\u1ea1ng v\u00e0 v\u00f4 c\u00f9ng ph\u1ed5 bi\u1ebfn trong h\u00ecnh h\u1ecdc. N\u00f3 c\u00f3 \u0111\u1eb7c \u0111i\u1ec3m ch\u00ednh l\u00e0 \u0111\u1ed9 d\u00e0i c\u00e1c c\u1ea1nh v\u00e0 s\u1ed1 \u0111o c\u1ee7a c\u00e1c g\u00f3c kh\u00f4ng b\u1eb1ng nhau. \u0110i\u1ec1u n\u00e0y t\u1ea1o ra nhi\u1ec1u c\u00e1ch t\u00ednh di\u1ec7n t\u00edch kh\u00e1c nhau t\u00f9y thu\u1ed9c v\u00e0o th\u00f4ng tin c\u00f3 s\u1eb5n v\u1ec1 tam gi\u00e1c.<\/span><\/p>\n<p><picture><source srcset=\"https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/webp-express\/webp-images\/uploads\/2023\/12\/dien-tich-tam-giac-5.jpg.webp 800w, https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/webp-express\/webp-images\/uploads\/2023\/12\/dien-tich-tam-giac-5-300x169.jpg.webp 300w, https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/webp-express\/webp-images\/uploads\/2023\/12\/dien-tich-tam-giac-5-768x432.jpg.webp 768w\" sizes=\"(max-width: 800px) 100vw, 800px\" type=\"image\/webp\"><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter wp-image-300594 size-full webpexpress-processed\" src=\"https:\\\/\\\/hoanghamobile.com\/tin-tuc\/wp-content\/uploads\/2023\/12\/dien-tich-tam-giac-5.jpg\" alt=\"dien-tich-tam-giac-5\" width=\"800\" height=\"450\" srcset=\"https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/uploads\/2023\/12\/dien-tich-tam-giac-5.jpg 800w, https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/uploads\/2023\/12\/dien-tich-tam-giac-5-300x169.jpg 300w, https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/uploads\/2023\/12\/dien-tich-tam-giac-5-768x432.jpg 768w\" sizes=\"(max-width: 800px) 100vw, 800px\"><\/picture><\/p>\n<p><span style=\"font-weight: 400;\">Theo \u0111\u00f3, c\u00e1ch t\u00ednh di\u1ec7n t\u00edch ABC \u0111\u01a1n gi\u1ea3n nh\u1ea5t l\u00e0 s\u1eed d\u1ee5ng \u0111\u1ed9 d\u00e0i c\u1ee7a m\u1ed9t c\u1ea1nh b\u1ea5t k\u1ef3 nh\u00e2n v\u1edbi chi\u1ec1u cao t\u01b0\u01a1ng \u1ee9ng c\u1ee7a c\u1ea1nh \u0111\u00f3 v\u00e0 chia cho 2<\/span><\/p>\n<ul>\n<li style=\"font-weight: 400;\"><span style=\"font-weight: 400;\">S = (a x h) \/ 2<\/span><\/li>\n<\/ul>\n<p><span style=\"font-weight: 400;\">Ngo\u00e0i ra, b\u1ea1n c\u00f3 th\u1ec3 t\u00ednh <\/span><b>di\u1ec7n t\u00edch tam gi\u00e1c<\/b><span style=\"font-weight: 400;\"> th\u01b0\u1eddng b\u1eb1ng nh\u1eefng c\u00f4ng th\u1ee9c n\u00e2ng cao h\u01a1n. V\u00e0 c\u00f4ng th\u1ee9c Heron l\u00e0 m\u1ed9t trong nh\u1eefng c\u00e1ch t\u00ednh d\u1ef1a tr\u00ean \u0111\u1ed9 d\u00e0i ba c\u1ea1nh a, b, c v\u00e0 n\u1eeda chu vi c\u1ee7a tam gi\u00e1c.<\/span><\/p>\n<ul>\n<li style=\"font-weight: 400;\"><span style=\"font-weight: 400;\">S(ABC) = \u221a(p * (p \u2013 a) * (p \u2013 b) * (p \u2013 c)) \u00a0 Trong \u0111\u00f3: p = (a + b + c)\/2)<\/span><\/li>\n<\/ul>\n<p><span style=\"font-weight: 400;\">\u0110\u1ed1i v\u1edbi nh\u1eefng tr\u01b0\u1eddng h\u1ee3p c\u00f3 th\u00f4ng tin v\u1ec1 m\u1ed9t g\u00f3c v\u00e0 hai c\u1ea1nh trong tam gi\u00e1c ABC, th\u00ec \u0111\u1ecbnh l\u00fd Sine l\u00e0 m\u1ed9t ph\u01b0\u01a1ng ph\u00e1p ph\u00f9 h\u1ee3p \u0111\u1ec3 b\u1ea1n t\u00ednh di\u1ec7n t\u00edch:<\/span><\/p>\n<ul>\n<li style=\"font-weight: 400;\"><span style=\"font-weight: 400;\">S(ABC) = (1\/2) x a x b x Sin(C)<\/span><\/li>\n<\/ul>\n<h3><span style=\"font-weight: 400;\">Tam gi\u00e1c vu\u00f4ng<\/span><\/h3>\n<p><span style=\"font-weight: 400;\">C\u00f4ng th\u1ee9c t\u00ednh di\u1ec7n t\u00edch c\u1ee7a tam gi\u00e1c vu\u00f4ng r\u1ea5t \u0111\u01a1n gi\u1ea3n v\u00e0 d\u1ec5 \u00e1p d\u1ee5ng h\u01a1n so v\u1edbi tam gi\u00e1c th\u01b0\u1eddng. Theo \u0111\u00f3, c\u00e1ch t\u00ednh n\u00e0y s\u1ebd t\u1eadn d\u1ee5ng v\u00e0o vi\u1ec7c s\u1eed d\u1ee5ng chi\u1ec1u cao c\u00f3 s\u1eb5n c\u1ee7a tam gi\u00e1c vu\u00f4ng, m\u00e0 kh\u00f4ng c\u1ea7n b\u1ea1n ph\u1ea3i t\u00ecm \u0111\u01b0\u1eddng cao b\u1eb1ng c\u00e1ch v\u1ebd th\u00eam tr\u00ean h\u00ecnh v\u1ebd.<\/span><\/p>\n<p><picture><source srcset=\"https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/webp-express\/webp-images\/uploads\/2023\/12\/dien-tich-tam-giac-6.jpg.webp 800w, https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/webp-express\/webp-images\/uploads\/2023\/12\/dien-tich-tam-giac-6-300x169.jpg.webp 300w, https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/webp-express\/webp-images\/uploads\/2023\/12\/dien-tich-tam-giac-6-768x432.jpg.webp 768w\" sizes=\"(max-width: 800px) 100vw, 800px\" type=\"image\/webp\"><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter wp-image-300595 size-full webpexpress-processed\" src=\"https:\\\/\\\/hoanghamobile.com\/tin-tuc\/wp-content\/uploads\/2023\/12\/dien-tich-tam-giac-6.jpg\" alt=\"dien-tich-tam-giac-6\" width=\"800\" height=\"450\" srcset=\"https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/uploads\/2023\/12\/dien-tich-tam-giac-6.jpg 800w, https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/uploads\/2023\/12\/dien-tich-tam-giac-6-300x169.jpg 300w, https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/uploads\/2023\/12\/dien-tich-tam-giac-6-768x432.jpg 768w\" sizes=\"(max-width: 800px) 100vw, 800px\"><\/picture><\/p>\n<p><span style=\"font-weight: 400;\">\u0110\u1ed1i v\u1edbi tam gi\u00e1c vu\u00f4ng, c\u00f4ng th\u1ee9c t\u00ednh di\u1ec7n t\u00edch l\u00e0:<\/span><\/p>\n<ul>\n<li style=\"font-weight: 400;\"><span style=\"font-weight: 400;\">S = (A X H) \/ 2<\/span><\/li>\n<\/ul>\n<p><span style=\"font-weight: 400;\">\u1ede \u0111\u00e2y:<\/span><\/p>\n<ul>\n<li style=\"font-weight: 400;\"><span style=\"font-weight: 400;\">A l\u00e0 \u0111\u1ed9 d\u00e0i c\u1ee7a m\u1ed9t c\u1ea1nh g\u00f3c vu\u00f4ng (\u0111\u00e1y).<\/span><\/li>\n<li style=\"font-weight: 400;\"><span style=\"font-weight: 400;\">H l\u00e0 chi\u1ec1u cao t\u1eeb \u0111\u1ec9nh vu\u00f4ng g\u00f3c xu\u1ed1ng \u0111\u00e1y.<\/span><\/li>\n<\/ul>\n<h3><span style=\"font-weight: 400;\">Tam gi\u00e1c c\u00e2n<\/span><\/h3>\n<p><span style=\"font-weight: 400;\">Tam gi\u00e1c c\u00e2n s\u1edf h\u1eefu \u0111\u1eb7c t\u00ednh \u0111\u1eb7c bi\u1ec7t v\u1edbi hai c\u1ea1nh c\u00f3 \u0111\u1ed9 d\u00e0i b\u1eb1ng nhau v\u00e0 hai g\u00f3c \u0111\u1ed1i di\u1ec7n v\u1edbi nh\u1eefng c\u1ea1nh n\u00e0y c\u0169ng b\u1eb1ng nhau. \u0110\u1ec3 t\u00ednh <\/span><b>di\u1ec7n t\u00edch tam gi\u00e1c<\/b><span style=\"font-weight: 400;\"> c\u00e2n, ch\u00fang ta c\u00f3 th\u1ec3 s\u1eed d\u1ee5ng m\u1ed9t c\u00f4ng th\u1ee9c d\u1ef1a tr\u00ean chi\u1ec1u d\u00e0i c\u1ee7a c\u1ea1nh c\u00f2n l\u1ea1i v\u00e0 chi\u1ec1u cao t\u01b0\u01a1ng \u1ee9ng.<\/span><\/p>\n<ul>\n<li style=\"font-weight: 400;\"><span style=\"font-weight: 400;\">S = (A X H) \/ 2<\/span><\/li>\n<\/ul>\n<p><span style=\"font-weight: 400;\">Trong \u0111\u00f3:\u00a0<\/span><\/p>\n<ul>\n<li style=\"font-weight: 400;\"><span style=\"font-weight: 400;\">a l\u00e0 \u0111\u1ed9 d\u00e0i c\u1ee7a c\u1ea1nh c\u00f2n l\u1ea1i (kh\u00e1c v\u1edbi hai c\u1ea1nh c\u00f3 \u0111\u1ed9 d\u00e0i b\u1eb1ng nhau)\u00a0<\/span><\/li>\n<li style=\"font-weight: 400;\"><span style=\"font-weight: 400;\">h l\u00e0 chi\u1ec1u cao k\u1ebft h\u1ee3p t\u1eeb \u0111\u1ec9nh g\u00f3c \u0111\u1ed1i di\u1ec7n c\u1ee7a c\u1ea1nh \u0111\u00f3 xu\u1ed1ng \u0111\u00e1y.<\/span><\/li>\n<\/ul>\n<p><picture><source srcset=\"https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/webp-express\/webp-images\/uploads\/2023\/12\/dien-tich-tam-giac-7.jpg.webp 800w, https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/webp-express\/webp-images\/uploads\/2023\/12\/dien-tich-tam-giac-7-300x169.jpg.webp 300w, https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/webp-express\/webp-images\/uploads\/2023\/12\/dien-tich-tam-giac-7-768x432.jpg.webp 768w\" sizes=\"(max-width: 800px) 100vw, 800px\" type=\"image\/webp\"><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter wp-image-300596 size-full webpexpress-processed\" src=\"https:\\\/\\\/hoanghamobile.com\/tin-tuc\/wp-content\/uploads\/2023\/12\/dien-tich-tam-giac-7.jpg\" alt=\"dien-tich-tam-giac-7\" width=\"800\" height=\"450\" srcset=\"https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/uploads\/2023\/12\/dien-tich-tam-giac-7.jpg 800w, https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/uploads\/2023\/12\/dien-tich-tam-giac-7-300x169.jpg 300w, https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/uploads\/2023\/12\/dien-tich-tam-giac-7-768x432.jpg 768w\" sizes=\"(max-width: 800px) 100vw, 800px\"><\/picture><\/p>\n<p><span style=\"font-weight: 400;\">V\u00ed d\u1ee5 minh h\u1ecda cho c\u00e1ch t\u00ednh n\u00e0y: tam gi\u00e1c c\u00e2n ABC v\u1edbi hai c\u1ea1nh AB v\u00e0 AC c\u00f3 \u0111\u1ed9 d\u00e0i b\u1eb1ng nhau, c\u1ea1nh BC c\u00f3 \u0111\u1ed9 d\u00e0i 9cm. Chi\u1ec1u cao t\u1eeb \u0111\u1ec9nh A xu\u1ed1ng BC l\u00e0 5cm. \u0110\u1ec3 t\u00ednh di\u1ec7n t\u00edch ABC, ch\u00fang ta \u00e1p d\u1ee5ng c\u00f4ng th\u1ee9c:\u00a0<\/span><\/p>\n<p><span style=\"font-weight: 400;\">S(ABC) = \u00bd (9 * 5) = 22,5cm\u00b2.\u00a0<\/span><\/p>\n<h3><span style=\"font-weight: 400;\">Tam gi\u00e1c \u0111\u1ec1u<\/span><\/h3>\n<p><span style=\"font-weight: 400;\">Tam gi\u00e1c \u0111\u1ec1u l\u00e0 m\u1ed9t d\u1ea1ng \u0111\u1eb7c bi\u1ec7t, n\u1ed5i b\u1eadt v\u1edbi t\u00ednh ch\u1ea5t \u0111\u1ed3ng \u0111\u1ec1u trong c\u1ea3 c\u1ea1nh v\u00e0 g\u00f3c. Theo \u0111\u00f3, c\u00e1c c\u1ea1nh c\u1ee7a tam gi\u00e1c \u0111\u1ec1u c\u00f3 \u0111\u1ed9 d\u00e0i b\u1eb1ng nhau, c\u00f9ng v\u1edbi \u0111i\u1ec1u ki\u1ec7n t\u1ea5t c\u1ea3 c\u00e1c g\u00f3c \u0111\u1ec1u c\u00f3 \u0111\u1ed9 l\u1edbn ch\u00ednh x\u00e1c l\u00e0 60 \u0111\u1ed9. \u0110i\u1ec1u n\u00e0y t\u1ea1o ra m\u1ed9t s\u1ef1 c\u00e2n \u0111\u1ed1i ho\u00e0n h\u1ea3o v\u00e0 m\u1ed9t h\u00ecnh d\u00e1ng \u0111\u1ec1u \u0111\u1eb9p.<\/span><\/p>\n<p><span style=\"font-weight: 400;\">\u0110\u1ec3 t\u00ednh <\/span><b>di\u1ec7n t\u00edch tam gi\u00e1c<\/b><span style=\"font-weight: 400;\"> \u0111\u1ec1u c\u00f3 c\u1ea1nh \u0111\u1ed9 d\u00e0i a, ch\u00fang ta c\u00f3 th\u1ec3 s\u1eed d\u1ee5ng m\u1ed9t c\u00f4ng th\u1ee9c \u0111\u01a1n gi\u1ea3n d\u1ef1a tr\u00ean chi\u1ec1u cao v\u00e0 \u0111\u1ed9 d\u00e0i c\u1ea1nh \u0111\u00f3. S = (A X H) \/ 2<\/span><\/p>\n<p><span style=\"font-weight: 400;\">\u1ede \u0111\u00e2y:\u00a0<\/span><\/p>\n<ul>\n<li style=\"font-weight: 400;\"><span style=\"font-weight: 400;\">a l\u00e0 \u0111\u1ed9 d\u00e0i c\u1ee7a m\u1ed9t c\u1ea1nh b\u1ea5t k\u1ef3.<\/span><\/li>\n<li style=\"font-weight: 400;\"><span style=\"font-weight: 400;\">h l\u00e0 chi\u1ec1u cao \u1ee9ng v\u1edbi a.<\/span><\/li>\n<\/ul>\n<p><picture><source srcset=\"https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/webp-express\/webp-images\/uploads\/2023\/12\/dien-tich-tam-giac-8.jpg.webp 800w, https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/webp-express\/webp-images\/uploads\/2023\/12\/dien-tich-tam-giac-8-300x169.jpg.webp 300w, https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/webp-express\/webp-images\/uploads\/2023\/12\/dien-tich-tam-giac-8-768x432.jpg.webp 768w\" sizes=\"(max-width: 800px) 100vw, 800px\" type=\"image\/webp\"><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter wp-image-300597 size-full webpexpress-processed\" src=\"https:\\\/\\\/hoanghamobile.com\/tin-tuc\/wp-content\/uploads\/2023\/12\/dien-tich-tam-giac-8.jpg\" alt=\"dien-tich-tam-giac-8\" width=\"800\" height=\"450\" srcset=\"https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/uploads\/2023\/12\/dien-tich-tam-giac-8.jpg 800w, https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/uploads\/2023\/12\/dien-tich-tam-giac-8-300x169.jpg 300w, https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/uploads\/2023\/12\/dien-tich-tam-giac-8-768x432.jpg 768w\" sizes=\"(max-width: 800px) 100vw, 800px\"><\/picture><\/p>\n<p><span style=\"font-weight: 400;\">V\u00ed d\u1ee5 minh h\u1ecda cho vi\u1ec7c t\u00ednh di\u1ec7n t\u00edch c\u1ee7a tam gi\u00e1c ABC \u0111\u1ec1u v\u1edbi c\u00e1c c\u1ea1nh b\u1eb1ng nhau, m\u1ed7i c\u1ea1nh c\u00f3 \u0111\u1ed9 d\u00e0i 7cm v\u00e0 chi\u1ec1u cao t\u1eeb \u0111\u1ec9nh A xu\u1ed1ng c\u1ea1nh BC l\u00e0 6cm. B\u1eb1ng c\u00e1ch \u00e1p d\u1ee5ng c\u00f4ng th\u1ee9c, di\u1ec7n t\u00edch ABC \u0111\u01b0\u1ee3c t\u00ednh nh\u01b0 sau:\u00a0<\/span><\/p>\n<p><span style=\"font-weight: 400;\">S(ABC) = \u00bd (7 * 6) = 21cm\u00b2.\u00a0<\/span><\/p>\n<h3><span style=\"font-weight: 400;\">Tam gi\u00e1c trong h\u1ec7 t\u1ecda \u0111\u1ed9 Oxyz<\/span><\/h3>\n<p><span style=\"font-weight: 400;\">Trong kh\u00f4ng gian ba chi\u1ec1u v\u1edbi h\u1ec7 t\u1ecda \u0111\u1ed9 Oxyz, tam gi\u00e1c \u0111\u01b0\u1ee3c x\u00e1c \u0111\u1ecbnh b\u1edfi ba \u0111i\u1ec3m kh\u00f4ng c\u00f9ng n\u1eb1m tr\u00ean m\u1ed9t \u0111\u01b0\u1eddng th\u1eb3ng. S\u1ef1 v\u1ecb tr\u00ed c\u1ee7a c\u00e1c \u0111i\u1ec3m n\u00e0y \u0111\u01b0\u1ee3c bi\u1ec3u di\u1ec5n qua c\u00e1c t\u1ecda \u0111\u1ed9 (x, y, z), th\u1ec3 hi\u1ec7n v\u1ecb tr\u00ed c\u1ee7a \u0111i\u1ec3m trong kh\u00f4ng gian ba chi\u1ec1u.<\/span><\/p>\n<p><picture><source srcset=\"https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/webp-express\/webp-images\/uploads\/2023\/12\/dien-tich-tam-giac-9.jpg.webp 800w, https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/webp-express\/webp-images\/uploads\/2023\/12\/dien-tich-tam-giac-9-300x169.jpg.webp 300w, https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/webp-express\/webp-images\/uploads\/2023\/12\/dien-tich-tam-giac-9-768x432.jpg.webp 768w\" sizes=\"(max-width: 800px) 100vw, 800px\" type=\"image\/webp\"><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter wp-image-300598 size-full webpexpress-processed\" src=\"https:\\\/\\\/hoanghamobile.com\/tin-tuc\/wp-content\/uploads\/2023\/12\/dien-tich-tam-giac-9.jpg\" alt=\"dien-tich-tam-giac-9\" width=\"800\" height=\"450\" srcset=\"https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/uploads\/2023\/12\/dien-tich-tam-giac-9.jpg 800w, https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/uploads\/2023\/12\/dien-tich-tam-giac-9-300x169.jpg 300w, https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/uploads\/2023\/12\/dien-tich-tam-giac-9-768x432.jpg 768w\" sizes=\"(max-width: 800px) 100vw, 800px\"><\/picture><\/p>\n<p><span style=\"font-weight: 400;\">C\u00f4ng th\u1ee9c t\u00ednh <\/span><b>di\u1ec7n t\u00edch tam gi\u00e1c<\/b><span style=\"font-weight: 400;\"> trong h\u1ec7 tr\u1ee5c t\u1ecda \u0111\u1ed9 Oxyz r\u1ea5t \u0111\u1eb7c bi\u1ec7t. Di\u1ec7n t\u00edch n\u00e0y s\u1ebd \u0111\u01b0\u1ee3c t\u00ednh b\u1eb1ng n\u1eeda gi\u00e1 tr\u1ecb tuy\u1ec7t \u0111\u1ed1i c\u1ee7a t\u00edch h\u1ea1ng ba c\u1ee7a hai vect\u01a1 AB v\u00e0 AC.<\/span><\/p>\n<p><span style=\"font-weight: 400;\">\u0110\u1ec3 \u00e1p d\u1ee5ng c\u00f4ng th\u1ee9c n\u00e0y, ta c\u1ea7n bi\u1ec3u di\u1ec5n hai vect\u01a1 AB v\u00e0 AC tr\u00ean tr\u1ee5c Oxyz. V\u00ed d\u1ee5, cho tam gi\u00e1c ABC v\u1edbi c\u00e1c \u0111i\u1ec3m A(-1; 1; 2), B(1; 2; 3), v\u00e0 C(3; \u20132; 0) tr\u00ean h\u1ec7 t\u1ecda \u0111\u1ed9. Khi t\u00ednh to\u00e1n di\u1ec7n t\u00edch ABC, ch\u00fang ta s\u1eed d\u1ee5ng c\u00f4ng th\u1ee9c:<\/span><\/p>\n<p><span style=\"font-weight: 400;\">S = (I vecto AB x vecto AC I) \/ 2<\/span><\/p>\n<h3><span style=\"font-weight: 400;\">Tam gi\u00e1c n\u00e2ng cao<\/span><\/h3>\n<p><span style=\"font-weight: 400;\">B\u00ean c\u1ea1nh nh\u1eefng c\u00e1ch t\u00ednh \u0111\u00e3 c\u00f3 s\u1eb5n, \u0111\u1ec1 b\u00e0i c\u00f3 th\u1ec3 s\u1ebd cho m\u1ed9t s\u1ed1 d\u1ea1ng tam gi\u00e1c n\u00e2ng cao kh\u00e1c, v\u00e0 \u0111\u1ed3ng th\u1eddi c\u0169ng c\u00f3 th\u1ec3 c\u00f3 c\u00f4ng th\u1ee9c t\u00ednh di\u1ec7n t\u00edch c\u1ee5 th\u1ec3 d\u1ef1a tr\u00ean \u0111i\u1ec1u ki\u1ec7n c\u1ee5 th\u1ec3 c\u1ee7a tam gi\u00e1c. Ch\u00ednh v\u00ec th\u1ebf, t\u00f9y thu\u1ed9c v\u00e0o th\u00f4ng tin c\u1ee5 th\u1ec3 v\u1ec1 tam gi\u00e1c, b\u1ea1n c\u00f3 th\u1ec3 s\u1eed d\u1ee5ng c\u00e1c ph\u01b0\u01a1ng ph\u00e1p t\u00ednh di\u1ec7n t\u00edch t\u01b0\u01a1ng \u1ee9ng nh\u01b0 s\u1eed d\u1ee5ng \u0111\u1ecbnh l\u00ed cosin, sin ho\u1eb7c c\u00e1c ph\u01b0\u01a1ng ph\u00e1p kh\u00e1c t\u00f9y thu\u1ed9c v\u00e0o th\u00f4ng tin \u0111\u01b0\u1ee3c cung c\u1ea5p.<\/span><\/p>\n<p><picture><source srcset=\"https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/webp-express\/webp-images\/uploads\/2023\/12\/dien-tich-tam-giac-10.jpg.webp 800w, https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/webp-express\/webp-images\/uploads\/2023\/12\/dien-tich-tam-giac-10-300x169.jpg.webp 300w, https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/webp-express\/webp-images\/uploads\/2023\/12\/dien-tich-tam-giac-10-768x432.jpg.webp 768w\" sizes=\"(max-width: 800px) 100vw, 800px\" type=\"image\/webp\"><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter wp-image-300599 size-full webpexpress-processed\" src=\"https:\\\/\\\/hoanghamobile.com\/tin-tuc\/wp-content\/uploads\/2023\/12\/dien-tich-tam-giac-10.jpg\" alt=\"dien-tich-tam-giac-10\" width=\"800\" height=\"450\" srcset=\"https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/uploads\/2023\/12\/dien-tich-tam-giac-10.jpg 800w, https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/uploads\/2023\/12\/dien-tich-tam-giac-10-300x169.jpg 300w, https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/uploads\/2023\/12\/dien-tich-tam-giac-10-768x432.jpg 768w\" sizes=\"(max-width: 800px) 100vw, 800px\"><\/picture><\/p>\n<h2><span style=\"font-weight: 400;\">M\u1ed9t s\u1ed1 d\u1ea1ng b\u00e0i t\u00ednh di\u1ec7n t\u00edch tam gi\u00e1c th\u01b0\u1eddng g\u1eb7p<\/span><\/h2>\n<p><span style=\"font-weight: 400;\">Sau \u0111\u00e2y l\u00e0 m\u1ed9t s\u1ed1 d\u1ea1ng b\u00e0i to\u00e1n t\u00ednh di\u1ec7n t\u00edch c\u1ee7a tam gi\u00e1c m\u00e0 b\u1ea1n s\u1ebd th\u01b0\u1eddng g\u1eb7p trong qu\u00e1 tr\u00ecnh gi\u1ea3i to\u00e1n h\u00ecnh h\u1ecdc<\/span><\/p>\n<h3><span style=\"font-weight: 400;\">D\u1ea1ng 1: Khi bi\u1ebft \u0111\u01b0\u1ee3c chi\u1ec1u cao v\u00e0 \u0111\u1ed9 d\u00e0i \u0111\u00e1y<\/span><\/h3>\n<p><span style=\"font-weight: 400;\">Trong h\u00ecnh h\u1ecdc, b\u00e0i t\u1eadp t\u00ednh di\u1ec7n t\u00edch c\u1ee7a tam gi\u00e1c th\u00f4ng qua c\u00f4ng th\u1ee9c c\u01a1 b\u1ea3n l\u00e0 m\u1ed9t trong nh\u1eefng d\u1ea1ng b\u00e0i \u0111\u01a1n gi\u1ea3n v\u00e0 d\u1ec5 \u00e1p d\u1ee5ng nh\u1ea5t. C\u00f4ng th\u1ee9c c\u01a1 b\u1ea3n \u0111\u1ec3 t\u00ednh di\u1ec7n t\u00edch th\u01b0\u1eddng l\u00e0 S (ABC) = \u00bd (a*h)<\/span><\/p>\n<p><picture><source srcset=\"https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/webp-express\/webp-images\/uploads\/2023\/12\/dien-tich-tam-giac-11.jpg.webp 800w, https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/webp-express\/webp-images\/uploads\/2023\/12\/dien-tich-tam-giac-11-300x169.jpg.webp 300w, https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/webp-express\/webp-images\/uploads\/2023\/12\/dien-tich-tam-giac-11-768x432.jpg.webp 768w\" sizes=\"(max-width: 800px) 100vw, 800px\" type=\"image\/webp\"><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter wp-image-300600 size-full webpexpress-processed\" src=\"https:\\\/\\\/hoanghamobile.com\/tin-tuc\/wp-content\/uploads\/2023\/12\/dien-tich-tam-giac-11.jpg\" alt=\"dien-tich-tam-giac-11\" width=\"800\" height=\"450\" srcset=\"https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/uploads\/2023\/12\/dien-tich-tam-giac-11.jpg 800w, https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/uploads\/2023\/12\/dien-tich-tam-giac-11-300x169.jpg 300w, https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/uploads\/2023\/12\/dien-tich-tam-giac-11-768x432.jpg 768w\" sizes=\"(max-width: 800px) 100vw, 800px\"><\/picture><\/p>\n<p><span style=\"font-weight: 400;\">M\u1ed9t v\u00ed d\u1ee5 minh h\u1ecda: Tam gi\u00e1c ABC c\u00f3 \u0111\u1ed9 d\u00e0i c\u1ea1nh BC l\u00e0 40cm v\u00e0 chi\u1ec1u cao t\u01b0\u01a1ng \u1ee9ng v\u1edbi c\u1ea1nh \u0111\u00e1y BC l\u00e0 5cm. \u0110\u1ec3 t\u00ednh di\u1ec7n t\u00edch ABC, ch\u00fang ta s\u1eed d\u1ee5ng c\u00f4ng th\u1ee9c \u0111\u00e3 cho:\u00a0<\/span><\/p>\n<p><span style=\"font-weight: 400;\">S(ABC) = \u00bd (BC * h) = \u00bd (40 * 5) = 100 cm\u00b2<\/span><\/p>\n<h3><span style=\"font-weight: 400;\">D\u1ea1ng 2: Khi bi\u1ebft chi\u1ec1u cao v\u00e0 di\u1ec7n t\u00edch<\/span><\/h3>\n<p><span style=\"font-weight: 400;\">\u0110\u1ec3 t\u00ednh \u0111\u1ed9 d\u00e0i c\u1ee7a \u0111\u00e1y tam gi\u00e1c khi \u0111\u00e3 bi\u1ebft di\u1ec7n t\u00edch v\u00e0 chi\u1ec1u cao, ch\u00fang ta c\u00f3 th\u1ec3 \u00e1p d\u1ee5ng m\u1ed9t c\u00f4ng th\u1ee9c \u0111\u01a1n gi\u1ea3n. T\u1eeb c\u00f4ng th\u1ee9c t\u00ednh <\/span><b>di\u1ec7n t\u00edch tam gi\u00e1c<\/b><span style=\"font-weight: 400;\"> l\u00e0 S (ABC) = \u00bd (a*h), ch\u00fang ta c\u00f3 th\u1ec3 suy ra c\u00f4ng th\u1ee9c \u0111\u1ec3 t\u00ednh \u0111\u1ed9 d\u00e0i \u0111\u00e1y: a = (S x 2 )\/ h<\/span><\/p>\n<p><picture><source srcset=\"https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/webp-express\/webp-images\/uploads\/2023\/12\/dien-tich-tam-giac-12.jpg.webp 800w, https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/webp-express\/webp-images\/uploads\/2023\/12\/dien-tich-tam-giac-12-300x169.jpg.webp 300w, https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/webp-express\/webp-images\/uploads\/2023\/12\/dien-tich-tam-giac-12-768x432.jpg.webp 768w\" sizes=\"(max-width: 800px) 100vw, 800px\" type=\"image\/webp\"><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter wp-image-300601 size-full webpexpress-processed\" src=\"https:\\\/\\\/hoanghamobile.com\/tin-tuc\/wp-content\/uploads\/2023\/12\/dien-tich-tam-giac-12.jpg\" alt=\"dien-tich-tam-giac-12\" width=\"800\" height=\"450\" srcset=\"https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/uploads\/2023\/12\/dien-tich-tam-giac-12.jpg 800w, https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/uploads\/2023\/12\/dien-tich-tam-giac-12-300x169.jpg 300w, https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/uploads\/2023\/12\/dien-tich-tam-giac-12-768x432.jpg 768w\" sizes=\"(max-width: 800px) 100vw, 800px\"><\/picture><\/p>\n<p><span style=\"font-weight: 400;\">V\u00ed d\u1ee5 minh h\u1ecda: Ta c\u1ea7n t\u00ednh \u0111\u1ed9 d\u00e0i c\u1ea1nh \u0111\u00e1y c\u1ee7a m\u1ed9t tam gi\u00e1c c\u00f3 chi\u1ec1u cao l\u00e0 80cm v\u00e0 di\u1ec7n t\u00edch b\u1eb1ng 4800cm\u00b2.<\/span><\/p>\n<p><span style=\"font-weight: 400;\">Qua ph\u00e9p t\u00ednh, ta s\u1ebd c\u00f3:<\/span><\/p>\n<p><span style=\"font-weight: 400;\">S = (4800 x 2) \/ 80 = 120 (cm)<\/span><\/p>\n<p><span style=\"font-weight: 400;\">Do \u0111\u00f3, \u0111\u1ed9 d\u00e0i c\u1ee7a c\u1ea1nh \u0111\u00e1y c\u1ee7a tam gi\u00e1c l\u00e0 120cm.<\/span><\/p>\n<h3><span style=\"font-weight: 400;\">D\u1ea1ng 3: Khi bi\u1ebft \u0111\u1ed9 d\u00e0i \u0111\u00e1y v\u00e0 di\u1ec7n t\u00edch<\/span><\/h3>\n<p><span style=\"font-weight: 400;\">\u0110\u1ec3 t\u00ednh \u0111\u1ed9 d\u00e0i c\u1ee7a \u0111\u00e1y tam gi\u00e1c khi \u0111\u00e3 bi\u1ebft di\u1ec7n t\u00edch v\u00e0 chi\u1ec1u cao, ch\u00fang ta c\u00f3 th\u1ec3 \u00e1p d\u1ee5ng m\u1ed9t c\u00f4ng th\u1ee9c \u0111\u01a1n gi\u1ea3n. T\u1eeb c\u00f4ng th\u1ee9c t\u00ednh di\u1ec7n t\u00edch n\u00e0y l\u00e0 S (ABC) = \u00bd (a*h), ch\u00fang ta c\u00f3 th\u1ec3 suy ra c\u00f4ng th\u1ee9c t\u00ednh chi\u1ec1u cao: h = (S x 2)\/a<\/span><\/p>\n<p><picture><source srcset=\"https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/webp-express\/webp-images\/uploads\/2023\/12\/dien-tich-tam-giac-13.jpg.webp 800w, https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/webp-express\/webp-images\/uploads\/2023\/12\/dien-tich-tam-giac-13-300x169.jpg.webp 300w, https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/webp-express\/webp-images\/uploads\/2023\/12\/dien-tich-tam-giac-13-768x432.jpg.webp 768w\" sizes=\"(max-width: 800px) 100vw, 800px\" type=\"image\/webp\"><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter wp-image-300602 size-full webpexpress-processed\" src=\"https:\\\/\\\/hoanghamobile.com\/tin-tuc\/wp-content\/uploads\/2023\/12\/dien-tich-tam-giac-13.jpg\" alt=\"dien-tich-tam-giac-13\" width=\"800\" height=\"450\" srcset=\"https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/uploads\/2023\/12\/dien-tich-tam-giac-13.jpg 800w, https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/uploads\/2023\/12\/dien-tich-tam-giac-13-300x169.jpg 300w, https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/uploads\/2023\/12\/dien-tich-tam-giac-13-768x432.jpg 768w\" sizes=\"(max-width: 800px) 100vw, 800px\"><\/picture><\/p>\n<p><span style=\"font-weight: 400;\">V\u00ed d\u1ee5 c\u1ee5 th\u1ec3: Gi\u1ea3 s\u1eed ch\u00fang ta c\u1ea7n t\u00ednh chi\u1ec1u cao c\u1ee7a m\u1ed9t tam gi\u00e1c c\u00f3 \u0111\u1ed9 d\u00e0i c\u1ea1nh \u0111\u00e1y l\u00e0 50cm v\u00e0 di\u1ec7n t\u00edch l\u00e0 1125cm\u00b2.<\/span><\/p>\n<p><span style=\"font-weight: 400;\">\u00c1p d\u1ee5ng c\u00f4ng th\u1ee9c, ta c\u00f3:<\/span><\/p>\n<p><span style=\"font-weight: 400;\">h = (1125 x 2) \/ 50 = 45 (cm)<\/span><\/p>\n<p><span style=\"font-weight: 400;\">V\u1eady, chi\u1ec1u cao c\u1ee7a tam gi\u00e1c l\u00e0 45cm.<\/span><\/p>\n<h2><span style=\"font-weight: 400;\">L\u1eddi k\u1ebft<\/span><\/h2>\n<p><span style=\"font-weight: 400;\">Nh\u1edd v\u00e0o nh\u1eefng c\u00f4ng th\u1ee9c t\u00ednh <\/span><b>di\u1ec7n t\u00edch tam gi\u00e1c<\/b><span style=\"font-weight: 400;\"> d\u1ec5 hi\u1ec3u v\u00e0 ch\u00ednh x\u00e1c nh\u1ea5t \u1edf tr\u00ean, ch\u00fang ta \u0111\u00e3 c\u00f3 c\u01a1 h\u1ed9i t\u00ecm hi\u1ec3u s\u00e2u h\u01a1n v\u1ec1 h\u00ecnh h\u1ecdc v\u00e0 c\u0169ng nh\u01b0 c\u00e1ch \u00e1p d\u1ee5ng ch\u00fang trong t\u1eebng tr\u01b0\u1eddng h\u1ee3p c\u1ee5 th\u1ec3. \u0110\u1ed3ng th\u1eddi, vi\u1ec7c s\u1eed d\u1ee5ng nh\u1eefng c\u00f4ng th\u1ee9c n\u00e0y kh\u00f4ng ch\u1ec9 gi\u00fap b\u1ea1n nhanh ch\u00f3ng gi\u1ea3i quy\u1ebft c\u00e1c b\u00e0i to\u00e1n m\u1ed9t c\u00e1ch linh ho\u1ea1t, \u0111\u1ea1t \u0111i\u1ec3m s\u1ed1 cao nhanh ch\u00f3ng m\u00e0 c\u00f2n m\u1edf ra c\u00e1nh c\u1eeda cho s\u1ef1 s\u00e1ng t\u1ea1o v\u00e0 \u1ee9ng d\u1ee5ng trong nhi\u1ec1u l\u0129nh v\u1ef1c kh\u00e1c nhau.<\/span><\/p>\n<p><span style=\"font-weight: 400;\">XEM TH\u00caM:<\/span><\/p>\n<ul>\n<li class=\"elementor-heading-title elementor-size-default\"><strong><a href=\"https:\/\/hoanghamobile.com\/tin-tuc\/the-tich-khoi-cau\/\">C\u00f4ng th\u1ee9c t\u00ednh th\u1ec3 t\u00edch h\u00ecnh c\u1ea7u v\u00e0 di\u1ec7n t\u00edch h\u00ecnh c\u1ea7u<\/a><\/strong><\/li>\n<li class=\"elementor-heading-title elementor-size-default\"><strong><a href=\"https:\/\/hoanghamobile.com\/tin-tuc\/duong-cheo-hinh-vuong\/\">C\u00f4ng th\u1ee9c t\u00ednh \u0111\u01b0\u1eddng ch\u00e9o h\u00ecnh vu\u00f4ng, \u0111\u01b0\u1eddng ch\u00e9o h\u00ecnh ch\u1eef nh\u1eadt<\/a><\/strong><\/li>\n<\/ul>\n","protected":false},"excerpt":{"rendered":"<p>Trong h\u00ecnh h\u1ecdc l\u1edbp 5-12, c\u00e1c c\u00f4ng th\u1ee9c t\u00ednh di\u1ec7n t\u00edch tam gi\u00e1c l\u00e0 ki\u1ebfn th\u1ee9c c\u01a1 b\u1ea3n, gi\u00fap gi\u1ea3i quy\u1ebft nhanh b\u00e0i t\u1eadp v\u00e0 \u1ee9ng d\u1ee5ng th\u1ef1c t\u1ebf nh\u01b0 ki\u1ebfn tr\u00fac, \u0111o l\u01b0\u1eddng. B\u00e0i vi\u1ebft t\u1ed5ng h\u1ee3p \u0111\u1ea7y \u0111\u1ee7 c\u00e1c c\u00f4ng th\u1ee9c t\u00ednh di\u1ec7n t\u00edch tam gi\u00e1c chi ti\u1ebft 2025: tam gi\u00e1c th\u01b0\u1eddng, vu\u00f4ng, [&hellip;]<\/p>\n","protected":false},"author":65,"featured_media":300603,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[3910,30453],"tags":[],"class_list":["post-300589","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-kham-pha","category-kien-thuc"],"yoast_head":"<!-- This site is optimized with the Yoast SEO Premium plugin v27.3 (Yoast SEO v27.4) - https:\/\/yoast.com\/product\/yoast-seo-premium-wordpress\/ -->\n<title>C\u00e1c c\u00f4ng th\u1ee9c t\u00ednh di\u1ec7n t\u00edch tam gi\u00e1c \u0111\u1ea7y \u0111\u1ee7 nh\u1ea5t 2025 | Tam gi\u00e1c th\u01b0\u1eddng, vu\u00f4ng, c\u00e2n, \u0111\u1ec1u<\/title>\n<meta name=\"description\" content=\"T\u1ed5ng h\u1ee3p c\u00e1c c\u00f4ng th\u1ee9c t\u00ednh di\u1ec7n t\u00edch tam gi\u00e1c chi ti\u1ebft 2025: tam gi\u00e1c th\u01b0\u1eddng, vu\u00f4ng, c\u00e2n, \u0111\u1ec1u, Heron, Sin C, t\u1ecda \u0111\u1ed9 Oxyz. 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