<\/span><\/h2>\n\n\n\nH\u00ecnh tam gi\u00e1c l\u00e0 m\u1ed9t d\u1ea1ng h\u00ecnh h\u1ecdc ph\u1eb3ng \u0111\u01b0\u1ee3c t\u1ea1o th\u00e0nh b\u1edfi ba \u0111o\u1ea1n th\u1eb3ng n\u1ed1i ba \u0111i\u1ec3m kh\u00f4ng tr\u00f9ng nhau. Ba \u0111o\u1ea1n th\u1eb3ng n\u00e0y \u0111\u01b0\u1ee3c g\u1ecdi l\u00e0 ba c\u1ea1nh c\u1ee7a tam gi\u00e1c, c\u00f2n ba \u0111i\u1ec3m n\u1ed1i c\u00e1c c\u1ea1nh l\u1ea1i v\u1edbi nhau \u0111\u01b0\u1ee3c g\u1ecdi l\u00e0 ba \u0111\u1ec9nh. Tam gi\u00e1c l\u00e0 m\u1ed9t trong nh\u1eefng h\u00ecnh c\u01a1 b\u1ea3n nh\u1ea5t trong h\u00ecnh h\u1ecdc Euclid v\u00e0 th\u01b0\u1eddng \u0111\u01b0\u1ee3c xem l\u00e0 \u0111\u01a1n v\u1ecb nh\u1ecf nh\u1ea5t c\u1ee7a c\u00e1c h\u00ecnh \u0111a gi\u00e1c.<\/p>\n\n\n\n![\"Kh\u00e1i](\"https:\/\/phongvu.vn\/cong-nghe\/wp-content\/uploads\/2025\/03\/dien-tich-tam-giac-10-1024x640.jpg\" "\\"\\"")
Kh\u00e1i ni\u1ec7m v\u1ec1 h\u00ecnh tam gi\u00e1c.<\/figcaption><\/figure>\n\n\n\nM\u1ed9t \u0111\u1eb7c \u0111i\u1ec3m n\u1ed5i b\u1eadt c\u1ee7a tam gi\u00e1c l\u00e0 t\u1ed5ng s\u1ed1 \u0111o ba g\u00f3c trong lu\u00f4n lu\u00f4n b\u1eb1ng 180 \u0111\u1ed9. D\u00f9 c\u00f3 nhi\u1ec1u d\u1ea1ng kh\u00e1c nhau nh\u01b0 tam gi\u00e1c \u0111\u1ec1u, tam gi\u00e1c c\u00e2n, tam gi\u00e1c vu\u00f4ng hay tam gi\u00e1c t\u00f9, t\u1ea5t c\u1ea3 \u0111\u1ec1u tu\u00e2n theo nguy\u00ean l\u00fd t\u1ed5ng g\u00f3c n\u00e0y. Ngo\u00e0i ra, tam gi\u00e1c kh\u00f4ng th\u1ec3 b\u1ecb “g\u1eadp l\u1ea1i” hay t\u1ef1 c\u1eaft nhau, n\u00ean lu\u00f4n l\u00e0 m\u1ed9t h\u00ecnh \u0111\u01a1n v\u00e0 l\u1ed3i.<\/p>\n\n\n\n
<\/span>\u0110\u1eb7c \u0111i\u1ec3m, t\u00ednh ch\u1ea5t c\u1ee7a h\u00ecnh tam gi\u00e1c th\u01b0\u1eddng g\u1eb7p<\/strong><\/span><\/h2>\n\n\n\nD\u01b0\u1edbi \u0111\u00e2y l\u00e0 m\u1ed9t s\u1ed1 t\u00ednh ch\u1ea5t ti\u00eau bi\u1ec3u th\u01b0\u1eddng g\u1eb7p trong tam gi\u00e1c:<\/p>\n\n\n\n
\n- T\u1ed5ng ba g\u00f3c trong c\u1ee7a m\u1ed9t tam gi\u00e1c lu\u00f4n b\u1eb1ng 180 \u0111\u1ed9, b\u1ea5t k\u1ec3 h\u00ecnh d\u1ea1ng hay \u0111\u1ed9 d\u00e0i c\u00e1c c\u1ea1nh.<\/li>\n\n\n\n
- Chi\u1ec1u d\u00e0i c\u1ee7a m\u1ed9t c\u1ea1nh b\u1ea5t k\u1ef3 trong tam gi\u00e1c lu\u00f4n nh\u1ecf h\u01a1n t\u1ed5ng hai c\u1ea1nh c\u00f2n l\u1ea1i v\u00e0 l\u1edbn h\u01a1n hi\u1ec7u c\u1ee7a ch\u00fang. \u0110\u00e2y l\u00e0 \u0111i\u1ec1u ki\u1ec7n c\u1ea7n \u0111\u1ec3 ba \u0111o\u1ea1n th\u1eb3ng c\u00f3 th\u1ec3 t\u1ea1o th\u00e0nh m\u1ed9t tam gi\u00e1c.<\/li>\n\n\n\n
- Trong m\u1ed9t tam gi\u00e1c, c\u1ea1nh \u0111\u1ed1i di\u1ec7n v\u1edbi g\u00f3c l\u1edbn h\u01a1n s\u1ebd c\u00f3 \u0111\u1ed9 d\u00e0i l\u1edbn h\u01a1n, v\u00e0 ng\u01b0\u1ee3c l\u1ea1i, g\u00f3c \u0111\u1ed1i di\u1ec7n v\u1edbi c\u1ea1nh d\u00e0i h\u01a1n s\u1ebd c\u00f3 s\u1ed1 \u0111o l\u1edbn h\u01a1n. \u0110\u00e2y l\u00e0 m\u1ed1i quan h\u1ec7 t\u1ef7 l\u1ec7 gi\u1eefa c\u1ea1nh v\u00e0 g\u00f3c \u0111\u1ed1i di\u1ec7n.<\/li>\n\n\n\n
- Ba \u0111\u01b0\u1eddng cao (\u0111\u01b0\u1eddng th\u1eb3ng h\u1ea1 t\u1eeb m\u1ed7i \u0111\u1ec9nh v\u00e0 vu\u00f4ng g\u00f3c v\u1edbi c\u1ea1nh \u0111\u1ed1i di\u1ec7n) lu\u00f4n c\u1eaft nhau t\u1ea1i m\u1ed9t \u0111i\u1ec3m duy nh\u1ea5t, g\u1ecdi l\u00e0 tr\u1ef1c t\u00e2m c\u1ee7a tam gi\u00e1c.<\/li>\n<\/ul>\n\n\n\n
![\"\u0110\u1eb7c](\"https:\/\/phongvu.vn\/cong-nghe\/wp-content\/uploads\/2025\/03\/dien-tich-tam-giac-2-1024x640.jpg\" "\\"\\"")
\u0110\u1eb7c \u0111i\u1ec3m c\u1ee7a c\u00e1c lo\u1ea1i tam gi\u00e1c th\u01b0\u1eddng g\u1eb7p.<\/figcaption><\/figure>\n\n\n\n\n- Ba \u0111\u01b0\u1eddng trung tuy\u1ebfn (\u0111o\u1ea1n th\u1eb3ng n\u1ed1i m\u1ed9t \u0111\u1ec9nh v\u1edbi trung \u0111i\u1ec3m c\u1ea1nh \u0111\u1ed1i di\u1ec7n) c\u00f9ng \u0111\u1ed3ng quy t\u1ea1i m\u1ed9t \u0111i\u1ec3m \u0111\u01b0\u1ee3c g\u1ecdi l\u00e0 tr\u1ecdng t\u00e2m. Tr\u1ecdng t\u00e2m chia m\u1ed7i \u0111\u01b0\u1eddng trung tuy\u1ebfn th\u00e0nh hai ph\u1ea7n v\u1edbi t\u1ef7 l\u1ec7 2:1, trong \u0111\u00f3 \u0111o\u1ea1n g\u1ea7n \u0111\u1ec9nh d\u00e0i g\u1ea5p \u0111\u00f4i \u0111o\u1ea1n c\u00f2n l\u1ea1i. \u0110\u1ed3ng th\u1eddi, m\u1ed7i \u0111\u01b0\u1eddng trung tuy\u1ebfn chia tam gi\u00e1c th\u00e0nh hai ph\u1ea7n c\u00f3 di\u1ec7n t\u00edch b\u1eb1ng nhau.<\/li>\n\n\n\n
- Ba \u0111\u01b0\u1eddng trung tr\u1ef1c (\u0111\u01b0\u1eddng th\u1eb3ng vu\u00f4ng g\u00f3c v\u1edbi c\u1ea1nh t\u1ea1i trung \u0111i\u1ec3m) giao nhau t\u1ea1i t\u00e2m \u0111\u01b0\u1eddng tr\u00f2n ngo\u1ea1i ti\u1ebfp \u2013 \u0111i\u1ec3m c\u00e1ch \u0111\u1ec1u ba \u0111\u1ec9nh c\u1ee7a tam gi\u00e1c.<\/li>\n\n\n\n
- Ba \u0111\u01b0\u1eddng ph\u00e2n gi\u00e1c trong (chia m\u1ed7i g\u00f3c c\u1ee7a tam gi\u00e1c th\u00e0nh hai ph\u1ea7n b\u1eb1ng nhau) giao nhau t\u1ea1i t\u00e2m \u0111\u01b0\u1eddng tr\u00f2n n\u1ed9i ti\u1ebfp, t\u1ee9c \u0111i\u1ec3m c\u00e1ch \u0111\u1ec1u ba c\u1ea1nh v\u00e0 l\u00e0 t\u00e2m c\u1ee7a v\u00f2ng tr\u00f2n ti\u1ebfp x\u00fac v\u1edbi c\u1ea3 ba c\u1ea1nh c\u1ee7a tam gi\u00e1c t\u1eeb b\u00ean trong.<\/li>\n\n\n\n
- Ngo\u00e0i ra, \u0111\u01b0\u1eddng ph\u00e2n gi\u00e1c c\u1ee7a m\u1ed9t g\u00f3c trong tam gi\u00e1c s\u1ebd chia c\u1ea1nh \u0111\u1ed1i di\u1ec7n th\u00e0nh hai \u0111o\u1ea1n th\u1eb3ng c\u00f3 \u0111\u1ed9 d\u00e0i t\u1ef7 l\u1ec7 v\u1edbi hai c\u1ea1nh k\u1ec1 g\u00f3c \u0111\u00f3. T\u00ednh ch\u1ea5t n\u00e0y th\u01b0\u1eddng \u0111\u01b0\u1ee3c \u00e1p d\u1ee5ng \u0111\u1ec3 thi\u1ebft l\u1eadp c\u00e1c t\u1ef7 l\u1ec7 trong b\u00e0i to\u00e1n h\u00ecnh h\u1ecdc.<\/li>\n<\/ul>\n\n\n\n
<\/span>Ph\u00e2n bi\u1ec7t c\u00e1c lo\u1ea1i h\u00ecnh tam gi\u00e1c. C\u00f3 bao nhi\u00eau lo\u1ea1i?<\/strong><\/span><\/h2>\n\n\n\nH\u00ecnh tam gi\u00e1c l\u00e0 m\u1ed9t trong nh\u1eefng h\u00ecnh h\u1ecdc c\u01a1 b\u1ea3n nh\u01b0ng l\u1ea1i mang nhi\u1ec1u t\u00ednh ch\u1ea5t \u0111\u1eb7c bi\u1ec7t v\u00e0 quan tr\u1ecdng trong to\u00e1n h\u1ecdc. M\u1ed7i lo\u1ea1i tam gi\u00e1c \u0111\u1ec1u c\u00f3 nh\u1eefng \u0111\u1eb7c \u0111i\u1ec3m ri\u00eang, gi\u00fap ph\u00e2n bi\u1ec7t v\u00e0 \u00e1p d\u1ee5ng v\u00e0o b\u00e0i to\u00e1n ph\u00f9 h\u1ee3p. D\u01b0\u1edbi \u0111\u00e2y l\u00e0 m\u1ed9t s\u1ed1 lo\u1ea1i h\u00ecnh tam gi\u00e1c th\u01b0\u1eddng g\u1eb7p:<\/p>\n\n\n\n
\n- Tam gi\u00e1c \u0111\u1ec1u<\/strong> c\u00f3 ba c\u1ea1nh b\u1eb1ng nhau v\u00e0 ba g\u00f3c b\u1eb1ng nhau, m\u1ed7i g\u00f3c \u0111\u1ec1u c\u00f3 s\u1ed1 \u0111o l\u00e0 60\u00b0. \u0110\u00e2y l\u00e0 tam gi\u00e1c c\u00f3 t\u00ednh \u0111\u1ed1i x\u1ee9ng ho\u00e0n h\u1ea3o nh\u1ea5t.<\/li>\n\n\n\n
- Tam gi\u00e1c c\u00e2n<\/strong> c\u00f3 hai c\u1ea1nh b\u1eb1ng nhau v\u00e0 hai g\u00f3c \u1edf \u0111\u00e1y b\u1eb1ng nhau. \u0110\u01b0\u1eddng cao, \u0111\u01b0\u1eddng ph\u00e2n gi\u00e1c v\u00e0 \u0111\u01b0\u1eddng trung tuy\u1ebfn k\u1ebb t\u1eeb \u0111\u1ec9nh \u0111\u1ed1i di\u1ec7n \u0111\u00e1y s\u1ebd tr\u00f9ng nhau.<\/li>\n\n\n\n
- Tam gi\u00e1c vu\u00f4ng<\/strong> l\u00e0 tam gi\u00e1c c\u00f3 m\u1ed9t g\u00f3c vu\u00f4ng (90\u00b0). Trong tam gi\u00e1c vu\u00f4ng, \u0111\u1ecbnh l\u00fd Pythagoras \u0111\u01b0\u1ee3c \u00e1p d\u1ee5ng: b\u00ecnh ph\u01b0\u01a1ng c\u1ea1nh huy\u1ec1n b\u1eb1ng t\u1ed5ng b\u00ecnh ph\u01b0\u01a1ng hai c\u1ea1nh g\u00f3c vu\u00f4ng.<\/li>\n\n\n\n
- Tam gi\u00e1c t\u00f9<\/strong> c\u00f3 m\u1ed9t g\u00f3c l\u1edbn h\u01a1n 90\u00b0 v\u00e0 nh\u1ecf h\u01a1n 180\u00b0. C\u1ea1nh \u0111\u1ed1i di\u1ec7n v\u1edbi g\u00f3c t\u00f9 s\u1ebd l\u00e0 c\u1ea1nh d\u00e0i nh\u1ea5t.<\/li>\n<\/ul>\n\n\n\n
![\"Ph\u00e2n](\"https:\/\/phongvu.vn\/cong-nghe\/wp-content\/uploads\/2025\/03\/dien-tich-tam-giac-4-1024x640.jpg\" "\\"\\"")
Ph\u00e2n bi\u1ec7t c\u00e1c lo\u1ea1i h\u00ecnh tam gi\u00e1c.<\/figcaption><\/figure>\n\n\n\n<\/span>C\u00f4ng th\u1ee9c t\u00ednh di\u1ec7n t\u00edch tam gi\u00e1c k\u00e8m v\u00ed d\u1ee5 \u0111\u00fang, \u0111\u1ea7y \u0111\u1ee7 nh\u1ea5t <\/strong><\/span><\/h2>\n\n\n\nVi\u1ec7c n\u1eafm v\u1eefng c\u00e1c c\u00f4ng th\u1ee9c t\u00ednh di\u1ec7n t\u00edch tam gi\u00e1c kh\u00f4ng ch\u1ec9 gi\u00fap h\u1ecdc sinh gi\u1ea3i b\u00e0i ch\u00ednh x\u00e1c m\u00e0 c\u00f2n h\u1ed7 tr\u1ee3 t\u01b0 duy h\u00ecnh h\u1ecdc v\u00e0 \u00e1p d\u1ee5ng linh ho\u1ea1t trong nhi\u1ec1u d\u1ea1ng to\u00e1n kh\u00e1c nhau. D\u01b0\u1edbi \u0111\u00e2y l\u00e0 \u0111\u1ea7y \u0111\u1ee7 c\u00e1c c\u00f4ng th\u1ee9c t\u00ednh di\u1ec7n t\u00edch tam gi\u00e1c, \u0111i k\u00e8m v\u00ed d\u1ee5 minh h\u1ecda c\u1ee5 th\u1ec3, ch\u00ednh x\u00e1c v\u00e0 d\u1ec5 hi\u1ec3u, gi\u00fap b\u1ea1n d\u1ec5 ghi nh\u1edb v\u00e0 \u00e1p d\u1ee5ng trong th\u1ef1c t\u1ebf c\u0169ng nh\u01b0 trong c\u00e1c k\u1ef3 ki\u1ec3m tra. H\u00e3y c\u00f9ng Phong V\u0169 \u0111i\u1ec3m qua nh\u00e9.<\/p>\n\n\n\n
<\/span>C\u00e1ch t\u00ednh di\u1ec7n t\u00edch tam gi\u00e1c th\u01b0\u1eddng<\/strong><\/span><\/h3>\n\n\n\nTam gi\u00e1c th\u01b0\u1eddng l\u00e0 m\u1ed9t lo\u1ea1i tam gi\u00e1c c\u00f3 ba c\u1ea1nh v\u00e0 ba g\u00f3c kh\u00f4ng \u0111\u1ec1u nhau. V\u00ec v\u1eady, \u0111\u1ec3 t\u00ednh di\u1ec7n t\u00edch c\u1ee7a tam gi\u00e1c th\u01b0\u1eddng, ta kh\u00f4ng th\u1ec3 ch\u1ec9 s\u1eed d\u1ee5ng tr\u1ef1c ti\u1ebfp c\u00e1c c\u1ea1nh ho\u1eb7c g\u00f3c \u0111\u00e3 cho. Thay v\u00e0o \u0111\u00f3, c\u1ea7n v\u1ebd th\u00eam m\u1ed9t \u0111\u01b0\u1eddng vu\u00f4ng g\u00f3c t\u1eeb \u0111\u1ec9nh xu\u1ed1ng c\u1ea1nh \u0111\u1ed1i di\u1ec7n.<\/p>\n\n\n\n![\"T\u00ednh](\"https:\/\/phongvu.vn\/cong-nghe\/wp-content\/uploads\/2025\/03\/dien-tich-tam-giac-6-1024x640.jpg\" "\\"\\"")
T\u00ednh di\u1ec7n t\u00edch tam gi\u00e1c th\u01b0\u1eddng.<\/figcaption><\/figure>\n\n\n\nC\u00f4ng th\u1ee9c t\u00ednh di\u1ec7n t\u00edch c\u1ee7a tam gi\u00e1c th\u01b0\u1eddng nh\u01b0 sau: S = 1\/2 \u00d7 a \u00d7 h<\/p>\n\n\n\n
Trong \u0111\u00f3:<\/p>\n\n\n\n
\n- S l\u00e0 di\u1ec7n t\u00edch c\u1ee7a tam gi\u00e1c<\/li>\n\n\n\n
- a l\u00e0 \u0111\u1ed9 d\u00e0i c\u1ea1nh \u0111\u00e1y, t\u1eeb \u0111\u1ec9nh \u0111\u1ebfn c\u1ea1nh \u0111\u1ed1i di\u1ec7n<\/li>\n\n\n\n
- h l\u00e0 chi\u1ec1u cao, l\u00e0 kho\u1ea3ng c\u00e1ch t\u1eeb \u0111\u1ec9nh xu\u1ed1ng c\u1ea1nh \u0111\u00e1y<\/li>\n<\/ul>\n\n\n\n
V\u00ed d\u1ee5: Cho tam gi\u00e1c ABC c\u00f3 c\u1ea1nh \u0111\u00e1y BC d\u00e0i 10 cm, chi\u1ec1u cao h\u1ea1 t\u1eeb \u0111\u1ec9nh A xu\u1ed1ng BC l\u00e0 6 cm. H\u1ecfi di\u1ec7n t\u00edch tam gi\u00e1c ABC l\u00e0 bao nhi\u00eau?<\/p>\n\n\n\n
L\u1eddi gi\u1ea3i: Di\u1ec7n t\u00edch tam gi\u00e1c ABC = 1\/2 x 10 x 6 = 30 (cm\u00b2)<\/p>\n\n\n\n
<\/span>C\u00e1ch t\u00ednh di\u1ec7n t\u00edch tam gi\u00e1c vu\u00f4ng<\/strong><\/span><\/h3>\n\n\n\nTam gi\u00e1c vu\u00f4ng l\u00e0 lo\u1ea1i tam gi\u00e1c c\u00f3 m\u1ed9t g\u00f3c vu\u00f4ng (90 \u0111\u1ed9), v\u1edbi hai c\u1ea1nh vu\u00f4ng g\u00f3c t\u1ea1o th\u00e0nh g\u00f3c n\u00e0y. V\u00ed d\u1ee5: Trong tam gi\u00e1c ABC vu\u00f4ng t\u1ea1i A, g\u00f3c BAC = 90 \u0111\u1ed9 v\u00e0 AB, AC l\u00e0 hai c\u1ea1nh vu\u00f4ng g\u00f3c.<\/p>\n\n\n\n![\"T\u00ednh](\"https:\/\/phongvu.vn\/cong-nghe\/wp-content\/uploads\/2025\/03\/dien-tich-tam-giac-8-1-1024x640.jpg\" "\\"\\"")
T\u00ednh di\u1ec7n t\u00edch tam gi\u00e1c vu\u00f4ng.<\/figcaption><\/figure>\n\n\n\nC\u00f4ng th\u1ee9c t\u00ednh di\u1ec7n t\u00edch c\u1ee7a tam gi\u00e1c vu\u00f4ng \u0111\u01b0\u1ee3c x\u00e1c \u0111\u1ecbnh nh\u01b0 sau: S = 1\/2 \u00d7 a \u00d7 b<\/p>\n\n\n\n
Trong \u0111\u00f3:<\/p>\n\n\n\n
\n- S l\u00e0 di\u1ec7n t\u00edch c\u1ee7a tam gi\u00e1c vu\u00f4ng<\/li>\n\n\n\n
- a v\u00e0 b l\u00e0 \u0111\u1ed9 d\u00e0i c\u1ee7a hai c\u1ea1nh vu\u00f4ng g\u00f3c v\u1edbi nhau<\/li>\n<\/ul>\n\n\n\n
V\u00ed d\u1ee5: Cho tam gi\u00e1c vu\u00f4ng ABC c\u00f3 c\u1ea1nh g\u00f3c vu\u00f4ng AB d\u00e0i 6 cm, c\u1ea1nh g\u00f3c vu\u00f4ng AC d\u00e0i 8 cm. H\u1ecfi di\u1ec7n t\u00edch tam gi\u00e1c vu\u00f4ng ABC l\u00e0 bao nhi\u00eau?<\/p>\n\n\n\n
L\u1eddi gi\u1ea3i: Di\u1ec7n t\u00edch tam gi\u00e1c vu\u00f4ng ABC = 1\/2 x 6 x 8 = 24 (cm\u00b2)<\/p>\n\n\n\n
<\/span>C\u00e1ch t\u00ednh di\u1ec7n t\u00edch tam gi\u00e1c c\u00e2n<\/strong><\/span><\/h3>\n\n\n\nTam gi\u00e1c c\u00e2n l\u00e0 m\u1ed9t lo\u1ea1i tam gi\u00e1c c\u00f3 hai c\u1ea1nh \u0111\u1ed1i di\u1ec7n nhau c\u00f3 \u0111\u1ed9 d\u00e0i b\u1eb1ng nhau, v\u00e0 hai g\u00f3c k\u1ec1 v\u1edbi c\u1ea1nh c\u00f2n l\u1ea1i c\u0169ng c\u00f3 gi\u00e1 tr\u1ecb gi\u1ed1ng nhau. V\u00ed d\u1ee5: Trong tam gi\u00e1c ABC, n\u1ebfu tam gi\u00e1c n\u00e0y l\u00e0 tam gi\u00e1c c\u00e2n t\u1ea1i \u0111\u1ec9nh A, th\u00ec AB = AC v\u00e0 g\u00f3c ABC = g\u00f3c ACB.<\/p>\n\n\n\n![\"T\u00ednh](\"https:\/\/phongvu.vn\/cong-nghe\/wp-content\/uploads\/2025\/03\/dien-tich-tam-giac-7-1024x640.jpg\" "\\"\\"")
T\u00ednh di\u1ec7n t\u00edch tam gi\u00e1c c\u00e2n.<\/figcaption><\/figure>\n\n\n\nC\u00f4ng th\u1ee9c t\u00ednh di\u1ec7n t\u00edch c\u1ee7a tam gi\u00e1c c\u00e2n \u0111\u01b0\u1ee3c th\u1ec3 hi\u1ec7n nh\u01b0 sau: S = 1\/2 \u00d7 a \u00d7 h<\/p>\n\n\n\n
Trong \u0111\u00f3:<\/p>\n\n\n\n
\n- S l\u00e0 di\u1ec7n t\u00edch c\u1ee7a tam gi\u00e1c<\/li>\n\n\n\n
- a l\u00e0 \u0111\u1ed9 d\u00e0i c\u1ee7a c\u1ea1nh \u0111\u00e1y \u0111\u1ed1i di\u1ec7n v\u1edbi \u0111\u1ec9nh c\u00e2n<\/li>\n\n\n\n
- h l\u00e0 chi\u1ec1u cao v\u1ebd t\u1eeb \u0111\u1ec9nh c\u00e2n xu\u1ed1ng c\u1ea1nh \u0111\u00e1y<\/li>\n<\/ul>\n\n\n\n
V\u00ed d\u1ee5: Cho tam gi\u00e1c c\u00e2n ABC v\u1edbi c\u1ea1nh \u0111\u00e1y BC d\u00e0i 10 cm, chi\u1ec1u cao h\u1ea1 t\u1eeb \u0111\u1ec9nh A xu\u1ed1ng BC l\u00e0 8 cm. H\u1ecfi di\u1ec7n t\u00edch tam gi\u00e1c c\u00e2n ABC l\u00e0 bao nhi\u00eau?<\/p>\n\n\n\n
L\u1eddi gi\u1ea3i: Di\u1ec7n t\u00edch tam gi\u00e1c ABC = 1\/2 x 10 x 8 = 40 (cm\u00b2)<\/p>\n\n\n\n
<\/span>C\u00e1ch t\u00ednh di\u1ec7n t\u00edch tam gi\u00e1c \u0111\u1ec1u<\/strong><\/span><\/h3>\n\n\n\nTam gi\u00e1c \u0111\u1ec1u l\u00e0 m\u1ed9t lo\u1ea1i tam gi\u00e1c c\u00f3 ba c\u1ea1nh v\u00e0 ba g\u00f3c \u0111\u1ec1u c\u00f3 gi\u00e1 tr\u1ecb b\u1eb1ng nhau. V\u00ed d\u1ee5: Trong tam gi\u00e1c ABC \u0111\u1ec1u, ta c\u00f3 AB = AC = BC v\u00e0 g\u00f3c ABC = g\u00f3c ACB = g\u00f3c BAC.<\/p>\n\n\n\n![\"T\u00ednh](\"https:\/\/phongvu.vn\/cong-nghe\/wp-content\/uploads\/2025\/03\/dien-tich-tam-giac-3-1024x640.jpg\" "\\"\\"")
T\u00ednh di\u1ec7n t\u00edch tam gi\u00e1c \u0111\u1ec1u.<\/figcaption><\/figure>\n\n\n\nC\u00f4ng th\u1ee9c t\u00ednh di\u1ec7n t\u00edch tam gi\u00e1c \u0111\u1ec1u \u0111\u01b0\u1ee3c tr\u00ecnh b\u00e0y nh\u01b0 sau: S = 1\/2 \u00d7 a \u00d7 h<\/p>\n\n\n\n
Trong \u0111\u00f3:<\/p>\n\n\n\n
\n- S l\u00e0 di\u1ec7n t\u00edch c\u1ee7a tam gi\u00e1c<\/li>\n\n\n\n
- a l\u00e0 \u0111\u1ed9 d\u00e0i c\u1ee7a c\u1ea1nh \u0111\u00e1y<\/li>\n\n\n\n
- h l\u00e0 chi\u1ec1u cao t\u1eeb \u0111\u1ec9nh xu\u1ed1ng c\u1ea1nh \u0111\u00e1y<\/li>\n<\/ul>\n\n\n\n
B\u00ean c\u1ea1nh \u0111\u00f3, b\u1eb1ng c\u00e1ch \u00e1p d\u1ee5ng \u0111\u1ecbnh l\u00fd Heron, ta c\u0169ng c\u00f3 th\u1ec3 t\u00ednh di\u1ec7n t\u00edch tam gi\u00e1c \u0111\u1ec1u b\u1eb1ng c\u00f4ng th\u1ee9c sau: S = a\u00b2 \u00d7 \u221a3 \/ 4<\/p>\n\n\n\n
V\u00ed d\u1ee5: Cho tam gi\u00e1c \u0111\u1ec1u ABC c\u00f3 c\u1ea1nh AB d\u00e0i 6 cm. H\u1ecfi di\u1ec7n t\u00edch tam gi\u00e1c \u0111\u1ec1u ABC l\u00e0 bao nhi\u00eau?<\/p>\n\n\n\n
L\u1eddi gi\u1ea3i: Di\u1ec7n t\u00edch tam gi\u00e1c ABC = 6\u00b2 \u00d7 \u221a3 \/ 4 \u200b\u2248 15.59 (cm\u00b2)<\/p>\n\n\n\n
<\/span>C\u00e1ch t\u00ednh di\u1ec7n t\u00edch tam gi\u00e1c vu\u00f4ng c\u00e2n<\/strong><\/span><\/h3>\n\n\n\nTam gi\u00e1c vu\u00f4ng c\u00e2n l\u00e0 lo\u1ea1i tam gi\u00e1c c\u00f3 m\u1ed9t g\u00f3c vu\u00f4ng (90 \u0111\u1ed9) v\u00e0 hai c\u1ea1nh k\u1ec1 v\u1edbi g\u00f3c vu\u00f4ng c\u00f3 \u0111\u1ed9 d\u00e0i b\u1eb1ng nhau. V\u00ed d\u1ee5: Trong tam gi\u00e1c ABC vu\u00f4ng t\u1ea1i A, g\u00f3c BAC = 90 \u0111\u1ed9 v\u00e0 AB = AC.<\/p>\n\n\n\n![\"T\u00ednh](\"https:\/\/phongvu.vn\/cong-nghe\/wp-content\/uploads\/2025\/03\/dien-tich-tam-giac-5-1024x640.jpg\" "\\"\\"")
T\u00ednh di\u1ec7n t\u00edch tam gi\u00e1c vu\u00f4ng c\u00e2n.<\/figcaption><\/figure>\n\n\n\nC\u00f4ng th\u1ee9c t\u00ednh di\u1ec7n t\u00edch c\u1ee7a tam gi\u00e1c vu\u00f4ng c\u00e2n \u0111\u01b0\u1ee3c x\u00e1c \u0111\u1ecbnh nh\u01b0 sau: S = 1\/2 \u00d7 a\u00b2<\/p>\n\n\n\n
Trong \u0111\u00f3:<\/p>\n\n\n\n
\n- S l\u00e0 di\u1ec7n t\u00edch c\u1ee7a tam gi\u00e1c vu\u00f4ng c\u00e2n<\/li>\n\n\n\n
- a l\u00e0 \u0111\u1ed9 d\u00e0i c\u1ee7a hai c\u1ea1nh k\u1ec1 v\u1edbi g\u00f3c vu\u00f4ng<\/li>\n<\/ul>\n\n\n\n
V\u00ed d\u1ee5: Cho tam gi\u00e1c vu\u00f4ng c\u00e2n ABC c\u00f3 2 c\u1ea1nh AB v\u00e0 AC d\u00e0i 6 cm. H\u1ecfi di\u1ec7n t\u00edch tam gi\u00e1c vu\u00f4ng c\u00e2n ABC l\u00e0 bao nhi\u00eau?<\/p>\n\n\n\n
L\u1eddi gi\u1ea3i: Di\u1ec7n t\u00edch tam gi\u00e1c ABC = 1\/2 \u00d7 6\u00b2 = 18 (cm\u00b2)<\/p>\n\n\n\n
<\/span>C\u00e1ch t\u00ednh di\u1ec7n t\u00edch tam gi\u00e1c trong h\u1ec7 t\u1ecda \u0111\u1ed9 Oxyz<\/strong><\/span><\/h3>\n\n\n\n![\"Tam](\"https:\/\/phongvu.vn\/cong-nghe\/wp-content\/uploads\/2025\/03\/dien-tich-tam-giac-8-1024x640.jpg\" "\\"\\"")
Tam gi\u00e1c trong h\u1ec7 t\u1ecda \u0111\u1ed9 Oxyz<\/figcaption><\/figure>\n\n\n\nTrong kh\u00f4ng gian 3 chi\u1ec1u v\u1edbi h\u1ec7 t\u1ecda \u0111\u1ed9 Oxyz, di\u1ec7n t\u00edch c\u1ee7a m\u1ed9t tam gi\u00e1c c\u00f3 th\u1ec3 t\u00ednh d\u1ef1a tr\u00ean c\u00e1c t\u1ecda \u0111\u1ed9 c\u1ee7a ba \u0111\u1ec9nh tam gi\u00e1c. N\u1ebfu tam gi\u00e1c c\u00f3 ba \u0111\u1ec9nh A(x1,y1,z1), B(x2,y2,z2) v\u00e0 C(x3,y3,z3), c\u00f4ng th\u1ee9c t\u00ednh di\u1ec7n t\u00edch c\u1ee7a tam gi\u00e1c n\u00e0y nh\u01b0 sau: <\/p>\n\n\n\n![\"T\u00ednh](\"https:\/\/phongvu.vn\/cong-nghe\/wp-content\/uploads\/2025\/03\/dien-tich-tam-giac-1-1024x640.jpg\" "\\"\\"")
T\u00ednh di\u1ec7n t\u00edch tam gi\u00e1c trong h\u1ec7 t\u1ecda \u0111\u1ed9 Oxyz.<\/figcaption><\/figure>\n\n\n\nV\u00ed d\u1ee5: Gi\u1ea3 s\u1eed tr\u00ean h\u1ec7 tr\u1ee5c t\u1ecda \u0111\u1ed9 Oxyz, ta c\u00f3 A(-2, 2, 1), B(1, 0, 2) v\u00e0 C(-1, 2, 3), \u00e1p d\u1ee5ng c\u00e1c b\u01b0\u1edbc t\u00ednh tr\u00ean ta s\u1ebd c\u00f3 k\u1ebft qu\u1ea3 di\u1ec7n t\u00edch tam gi\u00e1c ABC l\u00e0 \u221a24.5.<\/p>\n\n\n\n
<\/span>M\u1ed9t s\u1ed1 l\u01b0u \u00fd khi t\u00ednh di\u1ec7n t\u00edch tam gi\u00e1c<\/strong><\/span><\/h2>\n\n\n\nTr\u01b0\u1edbc khi \u00e1p d\u1ee5ng c\u00f4ng th\u1ee9c t\u00ednh di\u1ec7n t\u00edch, lu\u00f4n ki\u1ec3m tra xem c\u00e1c th\u00f4ng tin \u0111\u1ea7u v\u00e0o c\u00f3 h\u1ee3p l\u1ec7 kh\u00f4ng. V\u00ed d\u1ee5, c\u00e1c c\u1ea1nh c\u1ee7a tam gi\u00e1c ph\u1ea3i th\u1ecfa m\u00e3n b\u1ea5t \u0111\u1eb3ng th\u1ee9c tam gi\u00e1c (t\u1ed5ng \u0111\u1ed9 d\u00e0i hai c\u1ea1nh b\u1ea5t k\u1ef3 ph\u1ea3i l\u1edbn h\u01a1n c\u1ea1nh c\u00f2n l\u1ea1i). N\u1ebfu d\u1eef li\u1ec7u kh\u00f4ng h\u1ee3p l\u1ec7, b\u1ea1n s\u1ebd kh\u00f4ng th\u1ec3 t\u00ednh di\u1ec7n t\u00edch tam gi\u00e1c.<\/p>\n\n\n\n![\"L\u01b0u](\"https:\/\/phongvu.vn\/cong-nghe\/wp-content\/uploads\/2025\/03\/dien-tich-tam-giac-9-1024x640.jpg\" "\\"\\"")
L\u01b0u \u00fd khi t\u00ednh di\u1ec7n t\u00edch tam gi\u00e1c.<\/figcaption><\/figure>\n\n\n\nNgo\u00e0i ra, h\u00e3y ch\u00fa \u00fd \u0111\u1ebfn \u0111\u01a1n v\u1ecb \u0111o khi t\u00ednh di\u1ec7n t\u00edch, \u0111\u1eb7c bi\u1ec7t l\u00e0 khi c\u00e1c chi\u1ec1u d\u00e0i \u0111\u01b0\u1ee3c cho b\u1eb1ng \u0111\u01a1n v\u1ecb kh\u00e1c nhau (cm, m, inch,\u2026). \u0110\u1ea3m b\u1ea3o c\u00e1c gi\u00e1 tr\u1ecb nh\u1eadp v\u00e0o c\u00f9ng \u0111\u01a1n v\u1ecb ho\u1eb7c chuy\u1ec3n \u0111\u1ed5i ch\u00fang v\u1ec1 c\u00f9ng m\u1ed9t \u0111\u01a1n v\u1ecb tr\u01b0\u1edbc khi t\u00ednh to\u00e1n. Th\u00eam v\u00e0o \u0111\u00f3, khi t\u00ednh di\u1ec7n t\u00edch tam gi\u00e1c trong kh\u00f4ng gian 3D (h\u1ec7 t\u1ecda \u0111\u1ed9 Oxyz), b\u1ea1n c\u1ea7n t\u00ednh t\u00edch vector c\u1ee7a hai vector ch\u1ec9 ph\u01b0\u01a1ng c\u1ee7a c\u00e1c c\u1ea1nh tam gi\u00e1c. N\u1ebfu t\u00edch vector b\u1eb1ng 0, \u0111i\u1ec1u n\u00e0y c\u00f3 ngh\u0129a l\u00e0 ba \u0111i\u1ec3m c\u1ee7a tam gi\u00e1c n\u1eb1m tr\u00ean m\u1ed9t \u0111\u01b0\u1eddng th\u1eb3ng, v\u00e0 di\u1ec7n t\u00edch tam gi\u00e1c s\u1ebd b\u1eb1ng 0.<\/p>\n\n\n\n
<\/span>T\u1ed5ng k\u1ebft<\/strong><\/span><\/h2>\n\n\n\nNh\u01b0 v\u1eady, c\u00f3 th\u1ec3 th\u1ea5y r\u1eb1ng vi\u1ec7c n\u1eafm v\u1eefng c\u00e1c c\u00f4ng th\u1ee9c t\u00ednh di\u1ec7n t\u00edch tam gi\u00e1c l\u00e0 \u0111i\u1ec1u c\u1ea7n thi\u1ebft \u0111\u1ec3 gi\u1ea3i quy\u1ebft hi\u1ec7u qu\u1ea3 c\u00e1c d\u1ea1ng b\u00e0i t\u1eadp li\u00ean quan trong ch\u01b0\u01a1ng tr\u00ecnh h\u1ecdc. M\u1ed7i c\u00f4ng th\u1ee9c \u0111\u1ec1u ph\u00f9 h\u1ee3p v\u1edbi t\u1eebng d\u1ea1ng b\u00e0i v\u00e0 lo\u1ea1i d\u1eef ki\u1ec7n c\u1ee5 th\u1ec3, \u0111\u00f2i h\u1ecfi h\u1ecdc sinh ph\u1ea3i hi\u1ec3u r\u00f5 b\u1ea3n ch\u1ea5t v\u00e0 bi\u1ebft c\u00e1ch l\u1ef1a ch\u1ecdn ph\u01b0\u01a1ng ph\u00e1p ph\u00f9 h\u1ee3p. <\/p>\n\n\n\n
Hy v\u1ecdng r\u1eb1ng, qua b\u00e0i vi\u1ebft tr\u00ean, Phong V\u0169 \u0111\u00e3 cung c\u1ea5p cho b\u1ea1n m\u1ed9t c\u00e1i nh\u00ecn h\u1ec7 th\u1ed1ng, \u0111\u1ea7y \u0111\u1ee7 v\u00e0 ch\u00ednh x\u00e1c v\u1ec1 ch\u1ee7 \u0111\u1ec1 n\u00e0y. H\u00e3y luy\u1ec7n t\u1eadp th\u01b0\u1eddng xuy\u00ean k\u1ebft h\u1ee3p v\u1edbi vi\u1ec7c ghi nh\u1edb c\u00e1c c\u00f4ng th\u1ee9c \u0111\u1ec3 n\u00e2ng cao kh\u1ea3 n\u0103ng t\u01b0 duy v\u00e0 \u0111\u1ea1t k\u1ebft qu\u1ea3 t\u1ed1t h\u01a1n trong m\u00f4n To\u00e1n b\u1ea1n nh\u00e9!<\/p>\n","protected":false},"excerpt":{"rendered":"
Trong ch\u01b0\u01a1ng tr\u00ecnh to\u00e1n h\u1ecdc ph\u1ed5 th\u00f4ng, tam gi\u00e1c l\u00e0 m\u1ed9t d\u1ea1ng h\u00ecnh h\u1ecdc c\u01a1 b\u1ea3n nh\u01b0ng c\u00f3 t\u00ednh \u1ee9ng d\u1ee5ng cao trong c\u1ea3 l\u00fd thuy\u1ebft l\u1eabn th\u1ef1c ti\u1ec5n. Vi\u1ec7c t\u00ednh di\u1ec7n t\u00edch tam gi\u00e1c kh\u00f4ng ch\u1ec9 l\u00e0 ki\u1ebfn th\u1ee9c n\u1ec1n t\u1ea3ng trong m\u00f4n H\u00ecnh h\u1ecdc m\u00e0 c\u00f2n \u0111\u00f3ng vai tr\u00f2 quan tr\u1ecdng trong c\u00e1c […]<\/p>\n","protected":false},"author":13,"featured_media":122832,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"inline_featured_image":false},"categories":[24],"tags":[],"_links":{"self":[{"href":"https:\/\/phongvu.vn\/cong-nghe\/wp-json\/wp\/v2\/posts\/122035"}],"collection":[{"href":"https:\/\/phongvu.vn\/cong-nghe\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/phongvu.vn\/cong-nghe\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/phongvu.vn\/cong-nghe\/wp-json\/wp\/v2\/users\/13"}],"replies":[{"embeddable":true,"href":"https:\/\/phongvu.vn\/cong-nghe\/wp-json\/wp\/v2\/comments?post=122035"}],"version-history":[{"count":5,"href":"https:\/\/phongvu.vn\/cong-nghe\/wp-json\/wp\/v2\/posts\/122035\/revisions"}],"predecessor-version":[{"id":122831,"href":"https:\/\/phongvu.vn\/cong-nghe\/wp-json\/wp\/v2\/posts\/122035\/revisions\/122831"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/phongvu.vn\/cong-nghe\/wp-json\/wp\/v2\/media\/122832"}],"wp:attachment":[{"href":"https:\/\/phongvu.vn\/cong-nghe\/wp-json\/wp\/v2\/media?parent=122035"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/phongvu.vn\/cong-nghe\/wp-json\/wp\/v2\/categories?post=122035"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/phongvu.vn\/cong-nghe\/wp-json\/wp\/v2\/tags?post=122035"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}