{"id":122042,"date":"2025-03-25T07:00:23","date_gmt":"2025-03-25T00:00:23","guid":{"rendered":"https:\/\/phongvu.vn\/cong-nghe\/?p=122042"},"modified":"2025-03-26T11:28:14","modified_gmt":"2025-03-26T04:28:14","slug":"dien-tich-hinh-binh-hanh","status":"publish","type":"post","link":"https:\/\/phongvu.vn\/cong-nghe\/dien-tich-hinh-binh-hanh\/","title":{"rendered":"Di\u1ec7n t\u00edch h\u00ecnh b\u00ecnh h\u00e0nh: \u0110\u1ecbnh ngh\u0129a, c\u00f4ng th\u1ee9c v\u00e0 b\u00e0i t\u1eadp c\u00f3 l\u1eddi gi\u1ea3i"},"content":{"rendered":"\n<p>H\u00ecnh b\u00ecnh h\u00e0nh l\u00e0 m\u1ed9t trong nh\u1eefng h\u00ecnh h\u1ecdc ph\u1eb3ng quen thu\u1ed9c. Nh\u01b0ng b\u1ea1n hi\u1ec3u r\u00f5 v\u1ec1 \u0111\u1ecbnh ngh\u0129a, c\u00f4ng th\u1ee9c t\u00ednh di\u1ec7n t\u00edch h\u00ecnh b\u00ecnh h\u00e0nh v\u00e0 nh\u1eefng \u1ee9ng d\u1ee5ng th\u00fa v\u1ecb c\u1ee7a n\u00f3 trong \u0111\u1eddi s\u1ed1ng ch\u01b0a? B\u00e0i vi\u1ebft n\u00e0y <a href=\"https:\/\/phongvu.vn\/cong-nghe\/\" target=\"_blank\" rel=\"noreferrer noopener\">Phong V\u0169 Tech News<\/a> s\u1ebd gi\u00fap b\u1ea1n kh\u00e1m ph\u00e1 m\u1ed9t c\u00e1ch chi ti\u1ebft v\u00e0 d\u1ec5 hi\u1ec3u v\u1ec1 di\u1ec7n t\u00edch h\u00ecnh b\u00ecnh h\u00e0nh, t\u1eeb nh\u1eefng ki\u1ebfn th\u1ee9c c\u01a1 b\u1ea3n nh\u1ea5t \u0111\u1ebfn c\u00e1c b\u00e0i t\u1eadp v\u1eadn d\u1ee5ng c\u00f3 l\u1eddi gi\u1ea3i, m\u1edf ra nh\u1eefng g\u00f3c nh\u00ecn m\u1edbi v\u1ec1 h\u00ecnh h\u1ecdc.<\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\" \/>\n\n\n\n<ul>\n<li><a href=\"https:\/\/phongvu.vn\/cong-nghe\/dien-tich-hinh-thang\/\" target=\"_blank\" data-type=\"URL\" data-id=\"https:\/\/phongvu.vn\/cong-nghe\/dien-tich-hinh-thang\/\" rel=\"noreferrer noopener\">\u201cB\u1ecf t\u00fai\u201d 4 c\u00f4ng th\u1ee9c t\u00ednh di\u1ec7n t\u00edch h\u00ecnh thang (vu\u00f4ng, c\u00e2n, th\u01b0\u1eddng) k\u00e8m b\u00e0i t\u1eadp chu\u1ea9n nh\u1ea5t 2025<\/a><\/li>\n\n\n\n<li><a href=\"https:\/\/phongvu.vn\/cong-nghe\/cach-tinh-diem-trung-binh-mon-hk1-hk2-ca-nam\/\" target=\"_blank\" data-type=\"URL\" data-id=\"https:\/\/phongvu.vn\/cong-nghe\/cach-tinh-diem-trung-binh-mon-hk1-hk2-ca-nam\/\" rel=\"noreferrer noopener\">6 C\u00e1ch t\u00ednh \u0111i\u1ec3m trung b\u00ecnh m\u00f4n HK1, HK2, c\u1ea3 n\u0103m ch\u00ednh x\u00e1c k\u00e8m v\u00ed d\u1ee5<\/a><\/li>\n\n\n\n<li><a href=\"https:\/\/phongvu.vn\/cong-nghe\/cong-thuc-tinh-dien-tich-hinh-chu-nhat\/\" target=\"_blank\" data-type=\"URL\" data-id=\"https:\/\/phongvu.vn\/cong-nghe\/cong-thuc-tinh-dien-tich-hinh-chu-nhat\/\" rel=\"noreferrer noopener\">Di\u1ec7n t\u00edch h\u00ecnh ch\u1eef nh\u1eadt: \u0110\u1ecbnh ngh\u0129a, c\u00f4ng th\u1ee9c v\u00e0 b\u00e0i t\u1eadp c\u00f3 l\u1eddi gi\u1ea3i<\/a><\/li>\n<\/ul>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\" \/>\n\n\n\n<div id=\"ez-toc-container\" class=\"ez-toc-v2_0_55 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baseProfile=\"tiny\"><path d=\"M18.2 9.3l-6.2-6.3-6.2 6.3c-.2.2-.3.4-.3.7s.1.5.3.7c.2.2.4.3.7.3h11c.3 0 .5-.1.7-.3.2-.2.3-.5.3-.7s-.1-.5-.3-.7zM5.8 14.7l6.2 6.3 6.2-6.3c.2-.2.3-.5.3-.7s-.1-.5-.3-.7c-.2-.2-.4-.3-.7-.3h-11c-.3 0-.5.1-.7.3-.2.2-.3.5-.3.7s.1.5.3.7z\"\/><\/svg><\/span><\/span><\/label><input aria-label=\"Toggle\" aria-label=\"item-6a20c8ce561df\"  type=\"checkbox\" id=\"item-6a20c8ce561df\"><\/a><\/span><\/div>\n<nav><ul class='ez-toc-list ez-toc-list-level-1 ' ><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-1\" href=\"https:\/\/phongvu.vn\/cong-nghe\/dien-tich-hinh-binh-hanh\/#Dinh_nghia\" title=\"\u0110\u1ecbnh ngh\u0129a\">\u0110\u1ecbnh ngh\u0129a<\/a><ul class='ez-toc-list-level-3'><li class='ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-2\" href=\"https:\/\/phongvu.vn\/cong-nghe\/dien-tich-hinh-binh-hanh\/#Hinh_binh_hanh_la_gi\" title=\"H\u00ecnh b\u00ecnh h\u00e0nh l\u00e0 g\u00ec?&nbsp;\">H\u00ecnh b\u00ecnh h\u00e0nh l\u00e0 g\u00ec?&nbsp;<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-3\" href=\"https:\/\/phongvu.vn\/cong-nghe\/dien-tich-hinh-binh-hanh\/#Tinh_chat_cua_hinh_binh_hanh\" title=\"T\u00ednh ch\u1ea5t c\u1ee7a h\u00ecnh b\u00ecnh h\u00e0nh&nbsp;\">T\u00ednh ch\u1ea5t c\u1ee7a h\u00ecnh b\u00ecnh h\u00e0nh&nbsp;<\/a><\/li><\/ul><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-4\" href=\"https:\/\/phongvu.vn\/cong-nghe\/dien-tich-hinh-binh-hanh\/#Cong_thuc_tinh_dien_tich_hinh_binh_hanh\" title=\"C\u00f4ng th\u1ee9c t\u00ednh di\u1ec7n t\u00edch h\u00ecnh b\u00ecnh h\u00e0nh\">C\u00f4ng th\u1ee9c t\u00ednh di\u1ec7n t\u00edch h\u00ecnh b\u00ecnh h\u00e0nh<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-5\" href=\"https:\/\/phongvu.vn\/cong-nghe\/dien-tich-hinh-binh-hanh\/#Cac_bai_tap_co_loi_giai\" title=\"C\u00e1c b\u00e0i t\u1eadp c\u00f3 l\u1eddi gi\u1ea3i\">C\u00e1c b\u00e0i t\u1eadp c\u00f3 l\u1eddi gi\u1ea3i<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-6\" href=\"https:\/\/phongvu.vn\/cong-nghe\/dien-tich-hinh-binh-hanh\/#Ung_dung_thuc_te_cua_tinh_dien_tich_hinh_binh_hanh\" title=\"\u1ee8ng d\u1ee5ng th\u1ef1c t\u1ebf c\u1ee7a t\u00ednh di\u1ec7n t\u00edch h\u00ecnh b\u00ecnh h\u00e0nh\">\u1ee8ng d\u1ee5ng th\u1ef1c t\u1ebf c\u1ee7a t\u00ednh di\u1ec7n t\u00edch h\u00ecnh b\u00ecnh h\u00e0nh<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-7\" href=\"https:\/\/phongvu.vn\/cong-nghe\/dien-tich-hinh-binh-hanh\/#Tong_ket\" title=\"T\u1ed5ng k\u1ebft\">T\u1ed5ng k\u1ebft<\/a><\/li><\/ul><\/nav><\/div>\n<h2><span class=\"ez-toc-section\" id=\"Dinh_nghia\"><\/span><strong>\u0110\u1ecbnh ngh\u0129a<\/strong><span class=\"ez-toc-section-end\"><\/span><\/h2>\n\n\n\n<h3><span class=\"ez-toc-section\" id=\"Hinh_binh_hanh_la_gi\"><\/span><strong>H\u00ecnh b\u00ecnh h\u00e0nh l\u00e0 g\u00ec?&nbsp;<\/strong><span class=\"ez-toc-section-end\"><\/span><\/h3>\n\n\n\n<p>H\u00ecnh b\u00ecnh h\u00e0nh, trong h\u00ecnh h\u1ecdc Euclid, l\u00e0 m\u1ed9t t\u1ee9 gi\u00e1c \u0111\u01a1n gi\u1ea3n (kh\u00f4ng t\u1ef1 c\u1eaft nhau) v\u1edbi hai c\u1eb7p c\u1ea1nh \u0111\u1ed1i di\u1ec7n song song. C\u00e1c c\u1ea1nh \u0111\u1ed1i di\u1ec7n c\u1ee7a h\u00ecnh b\u00ecnh h\u00e0nh c\u00f3 chi\u1ec1u d\u00e0i b\u1eb1ng nhau v\u00e0 c\u00e1c g\u00f3c \u0111\u1ed1i di\u1ec7n c\u1ee7a h\u00ecnh b\u00ecnh h\u00e0nh c\u00f3 s\u1ed1 \u0111o b\u1eb1ng nhau. Thu\u1eadt ng\u1eef &#8220;h\u00ecnh b\u00ecnh h\u00e0nh&#8221; xu\u1ea5t ph\u00e1t t\u1eeb ti\u1ebfng Hy L\u1ea1p \u03c0\u03b1\u03c1\u03b1\u03bb\u03bb\u03b7\u03bb\u03cc\u03b3\u03c1\u03b1\u03bc\u03bc\u03bf (parall\u0113l\u00f3grammon), c\u00f3 ngh\u0129a l\u00e0 &#8220;h\u00ecnh d\u1ea1ng c\u1ee7a c\u00e1c \u0111\u01b0\u1eddng song song&#8221;. L\u1ea7n \u0111\u1ea7u ti\u00ean t\u1eeb n\u00e0y \u0111\u01b0\u1ee3c s\u1eed d\u1ee5ng trong ti\u1ebfng Anh l\u00e0 v\u00e0o n\u0103m 1570.<\/p>\n\n\n\n<figure class=\"wp-block-image size-full is-resized\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/phongvu.vn\/cong-nghe\/wp-content\/uploads\/2025\/03\/dien-tich-hinh-binh-hanh-2.jpg\" alt=\"H\u00ecnh b\u00ecnh h\u00e0nh \u0111\u01b0\u1ee3c \u0111\u1ecbnh ngh\u0129a l\u00e0 m\u1ed9t t\u1ee9 gi\u00e1c \u0111\u01a1n gi\u1ea3n, kh\u00f4ng t\u1ef1 c\u1eaft nhau, c\u00f3 hai c\u1eb7p c\u1ea1nh \u0111\u1ed1i di\u1ec7n song song v\u1edbi nhau\" class=\"wp-image-122045\" width=\"1024\" height=\"640\" srcset=\"https:\/\/phongvu.vn\/cong-nghe\/wp-content\/uploads\/2025\/03\/dien-tich-hinh-binh-hanh-2.jpg 1024w, https:\/\/phongvu.vn\/cong-nghe\/wp-content\/uploads\/2025\/03\/dien-tich-hinh-binh-hanh-2-300x188.jpg 300w, https:\/\/phongvu.vn\/cong-nghe\/wp-content\/uploads\/2025\/03\/dien-tich-hinh-binh-hanh-2-768x480.jpg 768w, https:\/\/phongvu.vn\/cong-nghe\/wp-content\/uploads\/2025\/03\/dien-tich-hinh-binh-hanh-2-150x94.jpg 150w, https:\/\/phongvu.vn\/cong-nghe\/wp-content\/uploads\/2025\/03\/dien-tich-hinh-binh-hanh-2-600x375.jpg 600w, https:\/\/phongvu.vn\/cong-nghe\/wp-content\/uploads\/2025\/03\/dien-tich-hinh-binh-hanh-2-696x435.jpg 696w, https:\/\/phongvu.vn\/cong-nghe\/wp-content\/uploads\/2025\/03\/dien-tich-hinh-binh-hanh-2-672x420.jpg 672w\" sizes=\"(max-width: 1024px) 100vw, 1024px\" title=\"\"><figcaption class=\"wp-element-caption\">H\u00ecnh b\u00ecnh h\u00e0nh \u0111\u01b0\u1ee3c \u0111\u1ecbnh ngh\u0129a l\u00e0 m\u1ed9t t\u1ee9 gi\u00e1c \u0111\u01a1n gi\u1ea3n, kh\u00f4ng t\u1ef1 c\u1eaft nhau, c\u00f3 hai c\u1eb7p c\u1ea1nh \u0111\u1ed1i di\u1ec7n song song v\u1edbi nhau<\/figcaption><\/figure>\n\n\n\n<h3><span class=\"ez-toc-section\" id=\"Tinh_chat_cua_hinh_binh_hanh\"><\/span><strong>T\u00ednh ch\u1ea5t c\u1ee7a h\u00ecnh b\u00ecnh h\u00e0nh&nbsp;<\/strong><span class=\"ez-toc-section-end\"><\/span><\/h3>\n\n\n\n<p>H\u00ecnh b\u00ecnh h\u00e0nh c\u00f3 nhi\u1ec1u t\u00ednh ch\u1ea5t \u0111\u1eb7c tr\u01b0ng. C\u00e1c c\u1ea1nh \u0111\u1ed1i di\u1ec7n c\u1ee7a n\u00f3 song song v\u00e0 b\u1eb1ng nhau. C\u00e1c g\u00f3c \u0111\u1ed1i di\u1ec7n c\u1ee7a h\u00ecnh b\u00ecnh h\u00e0nh th\u00ec b\u1eb1ng nhau, v\u00e0 hai g\u00f3c k\u1ec1 nhau th\u00ec b\u00f9 nhau, c\u00f3 t\u1ed5ng s\u1ed1 \u0111o l\u00e0 180 \u0111\u1ed9.&nbsp;<\/p>\n\n\n\n<p>Hai \u0111\u01b0\u1eddng ch\u00e9o c\u1ee7a h\u00ecnh b\u00ecnh h\u00e0nh c\u1eaft nhau t\u1ea1i trung \u0111i\u1ec3m c\u1ee7a m\u1ed7i \u0111\u01b0\u1eddng. M\u1ed7i \u0111\u01b0\u1eddng ch\u00e9o chia h\u00ecnh b\u00ecnh h\u00e0nh th\u00e0nh hai tam gi\u00e1c b\u1eb1ng nhau. \u0110\u1eb7c bi\u1ec7t, n\u1ebfu m\u1ed9t h\u00ecnh b\u00ecnh h\u00e0nh c\u00f3 m\u1ed9t g\u00f3c vu\u00f4ng, n\u00f3 tr\u1edf th\u00e0nh h\u00ecnh ch\u1eef nh\u1eadt.&nbsp;<\/p>\n\n\n\n<figure class=\"wp-block-image size-full is-resized\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/phongvu.vn\/cong-nghe\/wp-content\/uploads\/2025\/03\/dien-tich-hinh-binh-hanh-3.jpg\" alt=\"H\u00ecnh b\u00ecnh h\u00e0nh kh\u00f4ng ch\u1ec9 \u0111\u01a1n thu\u1ea7n l\u00e0 m\u1ed9t t\u1ee9 gi\u00e1c c\u00f3 c\u00e1c c\u1ea1nh \u0111\u1ed1i di\u1ec7n song song m\u00e0 c\u00f2n s\u1edf h\u1eefu nhi\u1ec1u t\u00ednh ch\u1ea5t quan tr\u1ecdng kh\u00e1\" class=\"wp-image-122046\" width=\"1024\" height=\"640\" srcset=\"https:\/\/phongvu.vn\/cong-nghe\/wp-content\/uploads\/2025\/03\/dien-tich-hinh-binh-hanh-3.jpg 1024w, https:\/\/phongvu.vn\/cong-nghe\/wp-content\/uploads\/2025\/03\/dien-tich-hinh-binh-hanh-3-300x188.jpg 300w, https:\/\/phongvu.vn\/cong-nghe\/wp-content\/uploads\/2025\/03\/dien-tich-hinh-binh-hanh-3-768x480.jpg 768w, https:\/\/phongvu.vn\/cong-nghe\/wp-content\/uploads\/2025\/03\/dien-tich-hinh-binh-hanh-3-150x94.jpg 150w, https:\/\/phongvu.vn\/cong-nghe\/wp-content\/uploads\/2025\/03\/dien-tich-hinh-binh-hanh-3-600x375.jpg 600w, https:\/\/phongvu.vn\/cong-nghe\/wp-content\/uploads\/2025\/03\/dien-tich-hinh-binh-hanh-3-696x435.jpg 696w, https:\/\/phongvu.vn\/cong-nghe\/wp-content\/uploads\/2025\/03\/dien-tich-hinh-binh-hanh-3-672x420.jpg 672w\" sizes=\"(max-width: 1024px) 100vw, 1024px\" title=\"\"><figcaption class=\"wp-element-caption\">H\u00ecnh b\u00ecnh h\u00e0nh kh\u00f4ng ch\u1ec9 \u0111\u01a1n thu\u1ea7n l\u00e0 m\u1ed9t t\u1ee9 gi\u00e1c c\u00f3 c\u00e1c c\u1ea1nh \u0111\u1ed1i di\u1ec7n song song m\u00e0 c\u00f2n s\u1edf h\u1eefu nhi\u1ec1u t\u00ednh ch\u1ea5t quan tr\u1ecdng kh\u00e1<\/figcaption><\/figure>\n\n\n\n<p>N\u1ebfu t\u1ea5t c\u1ea3 c\u00e1c c\u1ea1nh c\u1ee7a h\u00ecnh b\u00ecnh h\u00e0nh b\u1eb1ng nhau, n\u00f3 l\u00e0 h\u00ecnh thoi. H\u00ecnh vu\u00f4ng l\u00e0 m\u1ed9t tr\u01b0\u1eddng h\u1ee3p \u0111\u1eb7c bi\u1ec7t c\u1ee7a h\u00ecnh b\u00ecnh h\u00e0nh, v\u1eeba c\u00f3 c\u00e1c c\u1ea1nh b\u1eb1ng nhau v\u1eeba c\u00f3 c\u00e1c g\u00f3c vu\u00f4ng.&nbsp;&nbsp;<\/p>\n\n\n\n<h2><span class=\"ez-toc-section\" id=\"Cong_thuc_tinh_dien_tich_hinh_binh_hanh\"><\/span><strong>C\u00f4ng th\u1ee9c t\u00ednh di\u1ec7n t\u00edch h\u00ecnh b\u00ecnh h\u00e0nh<\/strong><span class=\"ez-toc-section-end\"><\/span><\/h2>\n\n\n\n<p>Di\u1ec7n t\u00edch c\u1ee7a h\u00ecnh b\u00ecnh h\u00e0nh c\u00f3 th\u1ec3 \u0111\u01b0\u1ee3c t\u00ednh b\u1eb1ng nhi\u1ec1u c\u00e1ch, t\u00f9y thu\u1ed9c v\u00e0o th\u00f4ng tin \u0111\u00e3 bi\u1ebft.<\/p>\n\n\n\n<p>C\u00f4ng th\u1ee9c c\u01a1 b\u1ea3n nh\u1ea5t \u0111\u1ec3 t\u00ednh di\u1ec7n t\u00edch h\u00ecnh b\u00ecnh h\u00e0nh l\u00e0 t\u00edch c\u1ee7a \u0111\u1ed9 d\u00e0i c\u1ea1nh \u0111\u00e1y (b) v\u00e0 chi\u1ec1u cao (h) t\u01b0\u01a1ng \u1ee9ng.&nbsp;<\/p>\n\n\n\n<p class=\"has-text-align-center\"><strong>Di\u1ec7n t\u00edch h\u00ecnh b\u00ecnh h\u00e0nh = b x h<\/strong><\/p>\n\n\n\n<figure class=\"wp-block-image size-full is-resized\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/phongvu.vn\/cong-nghe\/wp-content\/uploads\/2025\/03\/dien-tich-hinh-binh-hanh-4.jpg\" alt=\"Di\u1ec7n t\u00edch c\u1ee7a h\u00ecnh b\u00ecnh h\u00e0nh l\u00e0 ph\u1ea7n kh\u00f4ng gian \u0111\u01b0\u1ee3c bao b\u1ecdc b\u00ean trong b\u1ed1n c\u1ea1nh c\u1ee7a n\u00f3\" class=\"wp-image-122047\" width=\"1024\" height=\"640\" srcset=\"https:\/\/phongvu.vn\/cong-nghe\/wp-content\/uploads\/2025\/03\/dien-tich-hinh-binh-hanh-4.jpg 1024w, https:\/\/phongvu.vn\/cong-nghe\/wp-content\/uploads\/2025\/03\/dien-tich-hinh-binh-hanh-4-300x188.jpg 300w, https:\/\/phongvu.vn\/cong-nghe\/wp-content\/uploads\/2025\/03\/dien-tich-hinh-binh-hanh-4-768x480.jpg 768w, https:\/\/phongvu.vn\/cong-nghe\/wp-content\/uploads\/2025\/03\/dien-tich-hinh-binh-hanh-4-150x94.jpg 150w, https:\/\/phongvu.vn\/cong-nghe\/wp-content\/uploads\/2025\/03\/dien-tich-hinh-binh-hanh-4-600x375.jpg 600w, https:\/\/phongvu.vn\/cong-nghe\/wp-content\/uploads\/2025\/03\/dien-tich-hinh-binh-hanh-4-696x435.jpg 696w, https:\/\/phongvu.vn\/cong-nghe\/wp-content\/uploads\/2025\/03\/dien-tich-hinh-binh-hanh-4-672x420.jpg 672w\" sizes=\"(max-width: 1024px) 100vw, 1024px\" title=\"\"><figcaption class=\"wp-element-caption\">Di\u1ec7n t\u00edch c\u1ee7a h\u00ecnh b\u00ecnh h\u00e0nh l\u00e0 ph\u1ea7n kh\u00f4ng gian \u0111\u01b0\u1ee3c bao b\u1ecdc b\u00ean trong b\u1ed1n c\u1ea1nh c\u1ee7a n\u00f3<\/figcaption><\/figure>\n\n\n\n<p>Chi\u1ec1u cao l\u00e0 kho\u1ea3ng c\u00e1ch vu\u00f4ng g\u00f3c t\u1eeb c\u1ea1nh \u0111\u00e1y \u0111\u1ebfn c\u1ea1nh \u0111\u1ed1i di\u1ec7n. C\u00f4ng th\u1ee9c n\u00e0y t\u01b0\u01a1ng t\u1ef1 nh\u01b0 c\u00f4ng th\u1ee9c t\u00ednh di\u1ec7n t\u00edch h\u00ecnh ch\u1eef nh\u1eadt v\u00ec m\u1ed9t h\u00ecnh b\u00ecnh h\u00e0nh c\u00f3 th\u1ec3 \u0111\u01b0\u1ee3c bi\u1ebfn \u0111\u1ed5i th\u00e0nh h\u00ecnh ch\u1eef nh\u1eadt c\u00f3 c\u00f9ng \u0111\u00e1y v\u00e0 chi\u1ec1u cao m\u00e0 kh\u00f4ng thay \u0111\u1ed5i di\u1ec7n t\u00edch.<\/p>\n\n\n\n<p>Ngo\u00e0i ra, n\u1ebfu bi\u1ebft \u0111\u1ed9 d\u00e0i c\u1ee7a hai c\u1ea1nh k\u1ec1 nhau (a v\u00e0 b) v\u00e0 g\u00f3c xen gi\u1eefa (\u03b8), di\u1ec7n t\u00edch c\u00f3 th\u1ec3 \u0111\u01b0\u1ee3c t\u00ednh b\u1eb1ng c\u00f4ng th\u1ee9c: <strong>Di\u1ec7n t\u00edch = a \u00d7 b \u00d7 sin(\u03b8)<\/strong>. Khi bi\u1ebft \u0111\u1ed9 d\u00e0i hai \u0111\u01b0\u1eddng ch\u00e9o (d1 v\u00e0 d2) v\u00e0 g\u00f3c gi\u1eefa ch\u00fang (x), di\u1ec7n t\u00edch l\u00e0: <strong>Di\u1ec7n t\u00edch = \u00bd \u00d7 d1 \u00d7 d2 \u00d7 sin(x)<\/strong>. Trong h\u00ecnh h\u1ecdc vect\u01a1, n\u1ebfu hai c\u1ea1nh k\u1ec1 nhau \u0111\u01b0\u1ee3c bi\u1ec3u di\u1ec5n b\u1eb1ng vect\u01a1 <strong>a<\/strong> v\u00e0 <strong>b<\/strong>, di\u1ec7n t\u00edch l\u00e0 \u0111\u1ed9 l\u1edbn c\u1ee7a t\u00edch c\u00f3 h\u01b0\u1edbng:<strong> Di\u1ec7n t\u00edch =<\/strong> |<strong>a<\/strong> \u00d7 <strong>b<\/strong>|.<\/p>\n\n\n\n<p>=&gt; <strong>Xem th\u00eam: <\/strong><a href=\"https:\/\/phongvu.vn\/cong-nghe\/dien-tich-hinh-thang\/\" target=\"_blank\" rel=\"noreferrer noopener\">C\u00f4ng th\u1ee9c t\u00ednh di\u1ec7n t\u00edch h\u00ecnh thang k\u00e8m b\u00e0i t\u1eadp c\u00f3 l\u1eddi gi\u1ea3i<\/a><\/p>\n\n\n\n<h2><span class=\"ez-toc-section\" id=\"Cac_bai_tap_co_loi_giai\"><\/span><strong>C\u00e1c b\u00e0i t\u1eadp c\u00f3 l\u1eddi gi\u1ea3i<\/strong><span class=\"ez-toc-section-end\"><\/span><\/h2>\n\n\n\n<ol>\n<li><strong>T\u00ednh di\u1ec7n t\u00edch h\u00ecnh b\u00ecnh h\u00e0nh c\u00f3 c\u1ea1nh \u0111\u00e1y 15 cm v\u00e0 chi\u1ec1u cao 8 cm.<\/strong>\n<ul>\n<li>L\u1eddi gi\u1ea3i: Di\u1ec7n t\u00edch = 15 cm \u00d7 8 cm = 120 cm\u00b2.<\/li>\n<\/ul>\n<\/li>\n\n\n\n<li><strong>M\u1ed9t h\u00ecnh b\u00ecnh h\u00e0nh c\u00f3 hai c\u1ea1nh k\u1ec1 nhau d\u00e0i 7 cm v\u00e0 9 cm, g\u00f3c gi\u1eefa ch\u00fang l\u00e0 30 \u0111\u1ed9. T\u00ednh di\u1ec7n t\u00edch.<\/strong>\n<ul>\n<li>L\u1eddi gi\u1ea3i: Di\u1ec7n t\u00edch = 7 cm \u00d7 9 cm \u00d7 sin(30\u00b0) = 63 \u00d7 (1\/2) = 31.5 cm\u00b2.&nbsp;&nbsp;<\/li>\n<\/ul>\n<\/li>\n\n\n\n<li><strong>Di\u1ec7n t\u00edch h\u00ecnh b\u00ecnh h\u00e0nh l\u00e0 56 cm\u00b2, chi\u1ec1u cao l\u00e0 7 cm. T\u00ednh \u0111\u1ed9 d\u00e0i c\u1ea1nh \u0111\u00e1y.<\/strong>\n<ul>\n<li>L\u1eddi gi\u1ea3i: C\u1ea1nh \u0111\u00e1y = 56 cm\u00b2 \/ 7 cm = 8 cm.&nbsp;&nbsp;<\/li>\n<\/ul>\n<\/li>\n\n\n\n<li><strong>Cho h\u00ecnh b\u00ecnh h\u00e0nh c\u00f3 hai \u0111\u01b0\u1eddng ch\u00e9o d\u00e0i 10 cm v\u00e0 12 cm, g\u00f3c gi\u1eefa ch\u00fang l\u00e0 90 \u0111\u1ed9. T\u00ednh di\u1ec7n t\u00edch.<\/strong>\n<ul>\n<li>L\u1eddi gi\u1ea3i: Di\u1ec7n t\u00edch = \u00bd \u00d7 10 cm \u00d7 12 cm \u00d7 sin(90\u00b0) = \u00bd \u00d7 120 \u00d7 1 = 60 cm\u00b2.<\/li>\n<\/ul>\n<\/li>\n\n\n\n<li><strong>M\u1ed9t h\u00ecnh b\u00ecnh h\u00e0nh c\u00f3 c\u1ea1nh \u0111\u00e1y 10 cm v\u00e0 chi\u1ec1u cao 7 cm. T\u00ednh di\u1ec7n t\u00edch.<\/strong>\n<ul>\n<li>L\u1eddi gi\u1ea3i: Di\u1ec7n t\u00edch = 10 cm \u00d7 7 cm = 70 cm\u00b2.&nbsp;&nbsp;<\/li>\n<\/ul>\n<\/li>\n<\/ol>\n\n\n\n<h2><span class=\"ez-toc-section\" id=\"Ung_dung_thuc_te_cua_tinh_dien_tich_hinh_binh_hanh\"><\/span><strong>\u1ee8ng d\u1ee5ng th\u1ef1c t\u1ebf c\u1ee7a t\u00ednh di\u1ec7n t\u00edch h\u00ecnh b\u00ecnh h\u00e0nh<\/strong><span class=\"ez-toc-section-end\"><\/span><\/h2>\n\n\n\n<p>T\u00ednh di\u1ec7n t\u00edch h\u00ecnh b\u00ecnh h\u00e0nh c\u00f3 nhi\u1ec1u \u1ee9ng d\u1ee5ng trong th\u1ef1c t\u1ebf. Trong ki\u1ebfn tr\u00fac v\u00e0 x\u00e2y d\u1ef1ng, n\u00f3 \u0111\u01b0\u1ee3c d\u00f9ng \u0111\u1ec3 t\u00ednh to\u00e1n di\u1ec7n t\u00edch s\u00e0n, m\u00e1i nh\u00e0, c\u1eeda s\u1ed5 v\u00e0 c\u00e1c c\u1ea5u tr\u00fac kh\u00e1c. Trong k\u1ef9 thu\u1eadt v\u00e0 c\u01a1 kh\u00ed, quy t\u1eafc h\u00ecnh b\u00ecnh h\u00e0nh \u0111\u01b0\u1ee3c s\u1eed d\u1ee5ng \u0111\u1ec3 ph\u00e2n t\u00edch l\u1ef1c v\u00e0 vect\u01a1. Trong thi\u1ebft k\u1ebf n\u1ed9i th\u1ea5t, h\u00ecnh b\u00ecnh h\u00e0nh xu\u1ea5t hi\u1ec7n trong thi\u1ebft k\u1ebf b\u00e0n, k\u1ec7, t\u1ee7 v\u00e0 c\u00e1c v\u1eadt d\u1ee5ng kh\u00e1c. <\/p>\n\n\n\n<figure class=\"wp-block-image size-full is-resized\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/phongvu.vn\/cong-nghe\/wp-content\/uploads\/2025\/03\/dien-tich-hinh-binh-hanh-5.jpg\" alt=\"Vi\u1ec7c t\u00ednh to\u00e1n di\u1ec7n t\u00edch h\u00ecnh b\u00ecnh h\u00e0nh c\u00f2n c\u00f3 nhi\u1ec1u \u1ee9ng d\u1ee5ng thi\u1ebft th\u1ef1c trong cu\u1ed9c s\u1ed1ng h\u00e0ng ng\u00e0y v\u00e0 trong nhi\u1ec1u l\u0129nh v\u1ef1c kh\u00e1c nhau\" class=\"wp-image-122048\" width=\"1024\" height=\"640\" srcset=\"https:\/\/phongvu.vn\/cong-nghe\/wp-content\/uploads\/2025\/03\/dien-tich-hinh-binh-hanh-5.jpg 1024w, https:\/\/phongvu.vn\/cong-nghe\/wp-content\/uploads\/2025\/03\/dien-tich-hinh-binh-hanh-5-300x188.jpg 300w, https:\/\/phongvu.vn\/cong-nghe\/wp-content\/uploads\/2025\/03\/dien-tich-hinh-binh-hanh-5-768x480.jpg 768w, https:\/\/phongvu.vn\/cong-nghe\/wp-content\/uploads\/2025\/03\/dien-tich-hinh-binh-hanh-5-150x94.jpg 150w, https:\/\/phongvu.vn\/cong-nghe\/wp-content\/uploads\/2025\/03\/dien-tich-hinh-binh-hanh-5-600x375.jpg 600w, https:\/\/phongvu.vn\/cong-nghe\/wp-content\/uploads\/2025\/03\/dien-tich-hinh-binh-hanh-5-696x435.jpg 696w, https:\/\/phongvu.vn\/cong-nghe\/wp-content\/uploads\/2025\/03\/dien-tich-hinh-binh-hanh-5-672x420.jpg 672w\" sizes=\"(max-width: 1024px) 100vw, 1024px\" title=\"\"><figcaption class=\"wp-element-caption\">Vi\u1ec7c t\u00ednh to\u00e1n di\u1ec7n t\u00edch h\u00ecnh b\u00ecnh h\u00e0nh c\u00f2n c\u00f3 nhi\u1ec1u \u1ee9ng d\u1ee5ng thi\u1ebft th\u1ef1c trong cu\u1ed9c s\u1ed1ng h\u00e0ng ng\u00e0y v\u00e0 trong nhi\u1ec1u l\u0129nh v\u1ef1c kh\u00e1c nhau<\/figcaption><\/figure>\n\n\n\n<p>T\u1ea5m pin n\u0103ng l\u01b0\u1ee3ng m\u1eb7t tr\u1eddi c\u0169ng th\u01b0\u1eddng c\u00f3 d\u1ea1ng h\u00ecnh ch\u1eef nh\u1eadt ho\u1eb7c h\u00ecnh b\u00ecnh h\u00e0nh \u0111\u1ec3 d\u1ec5 l\u1eafp \u0111\u1eb7t tr\u00ean m\u00e1i nh\u00e0 d\u1ed1c. Trong \u0111o \u0111\u1ea1c \u0111\u1ea5t \u0111ai, ng\u01b0\u1eddi ta c\u00f3 th\u1ec3 \u01b0\u1edbc t\u00ednh di\u1ec7n t\u00edch c\u00e1c khu \u0111\u1ea5t c\u00f3 h\u00ecnh d\u1ea1ng g\u1ea7n gi\u1ed1ng h\u00ecnh b\u00ecnh h\u00e0nh. Ngo\u00e0i ra, h\u00ecnh b\u00ecnh h\u00e0nh c\u00f2n xu\u1ea5t hi\u1ec7n trong nhi\u1ec1u v\u1eadt d\u1ee5ng h\u00e0ng ng\u00e0y nh\u01b0 c\u1ee5c t\u1ea9y, g\u1ea1ch l\u00e1t s\u00e0n, v\u1edf, \u0111i\u1ec7n tho\u1ea1i th\u00f4ng minh, v\u00e0 b\u1eadc c\u1ea7u thang.&nbsp;&nbsp;<\/p>\n\n\n\n<h2><span class=\"ez-toc-section\" id=\"Tong_ket\"><\/span><strong>T\u1ed5ng k\u1ebft<\/strong><span class=\"ez-toc-section-end\"><\/span><\/h2>\n\n\n\n<p>H\u00ecnh b\u00ecnh h\u00e0nh l\u00e0 m\u1ed9t t\u1ee9 gi\u00e1c v\u1edbi c\u00e1c c\u1eb7p c\u1ea1nh \u0111\u1ed1i di\u1ec7n song song v\u00e0 b\u1eb1ng nhau, c\u00f9ng nhi\u1ec1u t\u00ednh ch\u1ea5t h\u00ecnh h\u1ecdc quan tr\u1ecdng. Di\u1ec7n t\u00edch c\u1ee7a h\u00ecnh b\u00ecnh h\u00e0nh c\u00f3 th\u1ec3 \u0111\u01b0\u1ee3c t\u00ednh b\u1eb1ng nhi\u1ec1u c\u00f4ng th\u1ee9c kh\u00e1c nhau t\u00f9y thu\u1ed9c v\u00e0o th\u00f4ng tin \u0111\u00e3 bi\u1ebft, v\u1edbi c\u00f4ng th\u1ee9c c\u01a1 b\u1ea3n l\u00e0 t\u00edch c\u1ee7a c\u1ea1nh \u0111\u00e1y v\u00e0 chi\u1ec1u cao. Vi\u1ec7c hi\u1ec3u r\u00f5 v\u00e0 bi\u1ebft c\u00e1ch t\u00ednh di\u1ec7n t\u00edch h\u00ecnh b\u00ecnh h\u00e0nh kh\u00f4ng ch\u1ec9 c\u1ea7n thi\u1ebft trong h\u1ecdc t\u1eadp m\u00e0 c\u00f2n c\u00f3 nhi\u1ec1u \u1ee9ng d\u1ee5ng thi\u1ebft th\u1ef1c trong \u0111\u1eddi s\u1ed1ng v\u00e0 c\u00e1c ng\u00e0nh ngh\u1ec1 kh\u00e1c nhau.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>H\u00ecnh b\u00ecnh h\u00e0nh l\u00e0 m\u1ed9t trong nh\u1eefng h\u00ecnh h\u1ecdc ph\u1eb3ng quen thu\u1ed9c. Nh\u01b0ng b\u1ea1n hi\u1ec3u r\u00f5 v\u1ec1 \u0111\u1ecbnh ngh\u0129a, c\u00f4ng th\u1ee9c t\u00ednh di\u1ec7n t\u00edch h\u00ecnh b\u00ecnh h\u00e0nh v\u00e0 nh\u1eefng \u1ee9ng d\u1ee5ng th\u00fa v\u1ecb c\u1ee7a n\u00f3 trong \u0111\u1eddi s\u1ed1ng ch\u01b0a? B\u00e0i vi\u1ebft n\u00e0y Phong V\u0169 Tech News s\u1ebd gi\u00fap b\u1ea1n kh\u00e1m ph\u00e1 m\u1ed9t c\u00e1ch chi ti\u1ebft [&hellip;]<\/p>\n","protected":false},"author":19,"featured_media":122044,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"inline_featured_image":false},"categories":[24,2663],"tags":[],"_links":{"self":[{"href":"https:\/\/phongvu.vn\/cong-nghe\/wp-json\/wp\/v2\/posts\/122042"}],"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\/19"}],"replies":[{"embeddable":true,"href":"https:\/\/phongvu.vn\/cong-nghe\/wp-json\/wp\/v2\/comments?post=122042"}],"version-history":[{"count":4,"href":"https:\/\/phongvu.vn\/cong-nghe\/wp-json\/wp\/v2\/posts\/122042\/revisions"}],"predecessor-version":[{"id":122486,"href":"https:\/\/phongvu.vn\/cong-nghe\/wp-json\/wp\/v2\/posts\/122042\/revisions\/122486"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/phongvu.vn\/cong-nghe\/wp-json\/wp\/v2\/media\/122044"}],"wp:attachment":[{"href":"https:\/\/phongvu.vn\/cong-nghe\/wp-json\/wp\/v2\/media?parent=122042"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/phongvu.vn\/cong-nghe\/wp-json\/wp\/v2\/categories?post=122042"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/phongvu.vn\/cong-nghe\/wp-json\/wp\/v2\/tags?post=122042"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}