{"id":36233,"date":"2023-11-17T16:52:04","date_gmt":"2023-11-17T16:52:04","guid":{"rendered":"https:\/\/www.splashlearn.com\/math-vocabulary\/?page_id=36233"},"modified":"2024-02-05T16:21:32","modified_gmt":"2024-02-05T16:21:32","slug":"area-of-triangle-in-determinant-form-definition-examples","status":"publish","type":"post","link":"https:\/\/www.splashlearn.com\/math-vocabulary\/area-of-triangle-in-determinant-form","title":{"rendered":"Area of Triangle in Determinant Form &#8211; Definition, Examples"},"content":{"rendered":"<div class=\"aioseo-breadcrumbs\"><span class=\"aioseo-breadcrumb\">\n\tMath-Vocabulary\n<\/span><\/div>\n\n<div class=\"ub_table-of-contents\" data-showtext=\"show\" data-hidetext=\"hide\" data-scrolltype=\"auto\" id=\"ub_table-of-contents-eaec2ff3-d874-4880-a95b-acd586f3fbed\" data-initiallyhideonmobile=\"false\"\n                    data-initiallyshow=\"true\"><div class=\"ub_table-of-contents-extra-container\"><div class=\"ub_table-of-contents-container ub_table-of-contents-1-column \"><ul><li><a href=https:\/\/www.splashlearn.com\/math-vocabulary\/area-of-triangle-in-determinant-form#0-what-is-the-area-of-a-triangle-in-determinant-form>What Is the Area of a Triangle in Determinant Form?<\/a><\/li><li><a href=https:\/\/www.splashlearn.com\/math-vocabulary\/area-of-triangle-in-determinant-form#1-formula-of-area-of-triangle-in-determinant-form>Formula of Area of Triangle in Determinant Form<\/a><\/li><li><a href=https:\/\/www.splashlearn.com\/math-vocabulary\/area-of-triangle-in-determinant-form#2-how-to-determine-the-area-of-triangle-in-determinant-form>How to Determine the Area of Triangle in Determinant Form<\/a><\/li><li><a href=https:\/\/www.splashlearn.com\/math-vocabulary\/area-of-triangle-in-determinant-form#5-solved-examples-on-area-of-triangle-in-determinant-form>Solved Examples on Area of Triangle in Determinant Form<\/a><\/li><li><a href=https:\/\/www.splashlearn.com\/math-vocabulary\/area-of-triangle-in-determinant-form#6-practice-problems-of-area-of-triangle-in-determinant-form>Practice Problems of Area of Triangle in Determinant Form<\/a><\/li><li><a href=https:\/\/www.splashlearn.com\/math-vocabulary\/area-of-triangle-in-determinant-form#7-frequently-asked-questions-about-the-area-of-triangle-in-determinant-form>Frequently Asked Questions about the Area of Triangle in Determinant Form<\/a><\/li><\/ul><\/div><\/div><\/div>\n\n\n<h2 class=\"wp-block-heading\" id=\"0-what-is-the-area-of-a-triangle-in-determinant-form\">What Is the Area of a Triangle in Determinant Form?<\/h2>\n\n\n\n<p><strong>In coordinate geometry, the <\/strong><a href=\"https:\/\/www.splashlearn.com\/math-vocabulary\/measurements\/area-and-perimeter-of-triangle\"><strong>area<\/strong><\/a><strong> of a triangle in determinant form can be calculated when the coordinates of the vertices of the <\/strong><a href=\"https:\/\/www.splashlearn.com\/math-vocabulary\/geometry\/triangle\"><strong>triangle<\/strong><\/a><strong> are provided. Calculating the area of a triangle in determinant form is an important application of determinants.<\/strong><\/p>\n\n\n\n<p>If the vertices of a triangle PQR are P(x<sub>1<\/sub>, y<sub>1<\/sub>), Q(x<sub>2<\/sub>, y<sub>2<\/sub>), and R(x<sub>3<\/sub>, y<sub>3<\/sub>), the area of the triangle can be calculated as follows:<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"620\" height=\"322\" src=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/11\/area-of-triangle-in-determinant-form-formula.png\" alt=\"Area of triangle in determinant form formula\" class=\"wp-image-36240\" title=\"Area of triangle in determinant form formula\" srcset=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/11\/area-of-triangle-in-determinant-form-formula.png 620w, https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/11\/area-of-triangle-in-determinant-form-formula-300x156.png 300w\" sizes=\"auto, (max-width: 620px) 100vw, 620px\" \/><\/figure>\n\n\n\n<p>Note that the process of expanding to find the determinant of a matrix remains consistent regardless of the chosen row or column. The result remains the same, making the choice of row or column arbitrary.<\/p>\n\n\n\n<p>Expanding the determinant along the first column, we get<\/p>\n\n\n\n<p>Area $= \\frac{1}{2} \\times \\left[x_{1} (y_{2} &#8211; y_{3}) + x_{2} (y_{3} &#8211; y_{1}) + x_{3} (y_{1} &#8211; y_{2})\\right]$<\/p>\n\n\n\n<p>A determinant of a square matrix A is a real value denoted by | A | or det (A). It is a scalar value held by every square matrix.&nbsp;<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"620\" height=\"385\" src=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/11\/solving-2-2-and-3-3-determinants.png\" alt=\"Solving 2 x 2 and 3 x 3 determinants\" class=\"wp-image-36241\" title=\"Solving 2 x 2 and 3 x 3 determinants\" srcset=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/11\/solving-2-2-and-3-3-determinants.png 620w, https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/11\/solving-2-2-and-3-3-determinants-300x186.png 300w\" sizes=\"auto, (max-width: 620px) 100vw, 620px\" \/><\/figure>\n\n\n\n<div id=\"recommended-games-container-id\" class=\"recommended-games-container\"><h4 class=\"recommended-games-container-headline\">Recommended Games<\/h4><div class=\"recommended-games-container-slides\"><div class=\"game-card-container-outer\">\r\n\t<a href=\"https:\/\/www.splashlearn.com\/s\/math-games\/add-multiples-of-100-in-unit-form\" data-vars-ga-category=\"splashlearn_vocab\" data-vars-ga-action=\"games_recommendations\" data-vars-ga-label=\"post_widget\">\r\n\t\t<div class=\"game-card-container-inner-block\">\r\n\t\t\t<img decoding=\"async\" class=\"game-card-container-inner-img\" src=\"https:\/\/cdn.splashmath.com\/curriculum_uploads\/images\/playables\/add_sub_pv_add_multiples_100_pt.png\" alt=\"Add Multiples of 100 in Unit Form Game\">\r\n\t\t<\/div>\r\n\t\r\n\t\t<div class=\"game-card-container-inner\">\r\n\t\t\t<div class=\"game-card-container-inner-name\">Add Multiples of 100 in Unit Form Game<\/div>\r\n\t\t\t<span class=\"game-card-container-inner-cta\">Play<\/span>\r\n\t\t<\/div>\r\n\t<\/a>\r\n<\/div><div class=\"game-card-container-outer\">\r\n\t<a href=\"https:\/\/www.splashlearn.com\/s\/math-games\/add-to-find-the-area\" data-vars-ga-category=\"splashlearn_vocab\" data-vars-ga-action=\"games_recommendations\" data-vars-ga-label=\"post_widget\">\r\n\t\t<div class=\"game-card-container-inner-block\">\r\n\t\t\t<img decoding=\"async\" class=\"game-card-container-inner-img\" src=\"https:\/\/cdn.splashmath.com\/curriculum_uploads\/images\/playables\/geo_meas_find_area_pt.png\" alt=\"Add to Find the Area Game\">\r\n\t\t<\/div>\r\n\t\r\n\t\t<div class=\"game-card-container-inner\">\r\n\t\t\t<div class=\"game-card-container-inner-name\">Add to Find the Area Game<\/div>\r\n\t\t\t<span class=\"game-card-container-inner-cta\">Play<\/span>\r\n\t\t<\/div>\r\n\t<\/a>\r\n<\/div><div class=\"game-card-container-outer\">\r\n\t<a href=\"https:\/\/www.splashlearn.com\/s\/math-games\/answer-questions-related-to-triangles\" data-vars-ga-category=\"splashlearn_vocab\" data-vars-ga-action=\"games_recommendations\" data-vars-ga-label=\"post_widget\">\r\n\t\t<div class=\"game-card-container-inner-block\">\r\n\t\t\t<img decoding=\"async\" class=\"game-card-container-inner-img\" src=\"https:\/\/cdn.splashmath.com\/curriculum_uploads\/images\/playables\/geometry_classify_tri_on_side_pt.png\" alt=\"Answer Questions Related to Triangles Game\">\r\n\t\t<\/div>\r\n\t\r\n\t\t<div class=\"game-card-container-inner\">\r\n\t\t\t<div class=\"game-card-container-inner-name\">Answer Questions Related to Triangles Game<\/div>\r\n\t\t\t<span class=\"game-card-container-inner-cta\">Play<\/span>\r\n\t\t<\/div>\r\n\t<\/a>\r\n<\/div><div class=\"game-card-container-outer\">\r\n\t<a href=\"https:\/\/www.splashlearn.com\/s\/math-games\/area-of-composite-figure\" data-vars-ga-category=\"splashlearn_vocab\" data-vars-ga-action=\"games_recommendations\" data-vars-ga-label=\"post_widget\">\r\n\t\t<div class=\"game-card-container-inner-block\">\r\n\t\t\t<img decoding=\"async\" class=\"game-card-container-inner-img\" src=\"https:\/\/cdn.splashmath.com\/curriculum_uploads\/images\/playables\/geo_meas_grannys_rescue_10_gm.png\" alt=\"Area of Composite Figure Game\">\r\n\t\t<\/div>\r\n\t\r\n\t\t<div class=\"game-card-container-inner\">\r\n\t\t\t<div class=\"game-card-container-inner-name\">Area of Composite Figure Game<\/div>\r\n\t\t\t<span class=\"game-card-container-inner-cta\">Play<\/span>\r\n\t\t<\/div>\r\n\t<\/a>\r\n<\/div><div class=\"game-card-container-outer\">\r\n\t<a href=\"https:\/\/www.splashlearn.com\/s\/math-games\/area-with-unit-squares-and-side-lengths\" data-vars-ga-category=\"splashlearn_vocab\" data-vars-ga-action=\"games_recommendations\" data-vars-ga-label=\"post_widget\">\r\n\t\t<div class=\"game-card-container-inner-block\">\r\n\t\t\t<img decoding=\"async\" class=\"game-card-container-inner-img\" src=\"https:\/\/cdn.splashmath.com\/curriculum_uploads\/images\/playables\/geo_meas_area_unit_sq_side_length_pt.png\" alt=\"Area with Unit Squares and Side Lengths Game\">\r\n\t\t<\/div>\r\n\t\r\n\t\t<div class=\"game-card-container-inner\">\r\n\t\t\t<div class=\"game-card-container-inner-name\">Area with Unit Squares and Side Lengths Game<\/div>\r\n\t\t\t<span class=\"game-card-container-inner-cta\">Play<\/span>\r\n\t\t<\/div>\r\n\t<\/a>\r\n<\/div><div class=\"game-card-container-outer\">\r\n\t<a href=\"https:\/\/www.splashlearn.com\/s\/math-games\/area-word-problems-on-product-of-fractions\" data-vars-ga-category=\"splashlearn_vocab\" data-vars-ga-action=\"games_recommendations\" data-vars-ga-label=\"post_widget\">\r\n\t\t<div class=\"game-card-container-inner-block\">\r\n\t\t\t<img decoding=\"async\" class=\"game-card-container-inner-img\" src=\"https:\/\/cdn.splashmath.com\/curriculum_uploads\/images\/playables\/fractions_real_life_prob_area_pt.png\" alt=\"Area Word Problems on Product of Fractions Game\">\r\n\t\t<\/div>\r\n\t\r\n\t\t<div class=\"game-card-container-inner\">\r\n\t\t\t<div class=\"game-card-container-inner-name\">Area Word Problems on Product of Fractions Game<\/div>\r\n\t\t\t<span class=\"game-card-container-inner-cta\">Play<\/span>\r\n\t\t<\/div>\r\n\t<\/a>\r\n<\/div><div class=\"game-card-container-outer\">\r\n\t<a href=\"https:\/\/www.splashlearn.com\/s\/math-games\/build-the-area\" data-vars-ga-category=\"splashlearn_vocab\" data-vars-ga-action=\"games_recommendations\" data-vars-ga-label=\"post_widget\">\r\n\t\t<div class=\"game-card-container-inner-block\">\r\n\t\t\t<img decoding=\"async\" class=\"game-card-container-inner-img\" src=\"https:\/\/cdn.splashmath.com\/curriculum_uploads\/images\/playables\/geo_meas_grannys_rescue_3_4_5_gm.png\" alt=\"Build the Area Game\">\r\n\t\t<\/div>\r\n\t\r\n\t\t<div class=\"game-card-container-inner\">\r\n\t\t\t<div class=\"game-card-container-inner-name\">Build the Area Game<\/div>\r\n\t\t\t<span class=\"game-card-container-inner-cta\">Play<\/span>\r\n\t\t<\/div>\r\n\t<\/a>\r\n<\/div><div class=\"game-card-container-outer\">\r\n\t<a href=\"https:\/\/www.splashlearn.com\/s\/math-games\/change-decimals-from-word-form-to-fraction-form\" data-vars-ga-category=\"splashlearn_vocab\" data-vars-ga-action=\"games_recommendations\" data-vars-ga-label=\"post_widget\">\r\n\t\t<div class=\"game-card-container-inner-block\">\r\n\t\t\t<img decoding=\"async\" class=\"game-card-container-inner-img\" src=\"https:\/\/cdn.splashmath.com\/curriculum_uploads\/images\/playables\/decimals_convert_words_to_frac_tenths_pt.png\" alt=\"Change Decimals from Word Form to Fraction Form Game\">\r\n\t\t<\/div>\r\n\t\r\n\t\t<div class=\"game-card-container-inner\">\r\n\t\t\t<div class=\"game-card-container-inner-name\">Change Decimals from Word Form to Fraction Form Game<\/div>\r\n\t\t\t<span class=\"game-card-container-inner-cta\">Play<\/span>\r\n\t\t<\/div>\r\n\t<\/a>\r\n<\/div><div class=\"game-card-container-outer\">\r\n\t<a href=\"https:\/\/www.splashlearn.com\/s\/math-games\/change-expanded-to-standard-form\" data-vars-ga-category=\"splashlearn_vocab\" data-vars-ga-action=\"games_recommendations\" data-vars-ga-label=\"post_widget\">\r\n\t\t<div class=\"game-card-container-inner-block\">\r\n\t\t\t<img decoding=\"async\" class=\"game-card-container-inner-img\" src=\"https:\/\/cdn.splashmath.com\/curriculum_uploads\/images\/playables\/place_value_expand_to_std_5d_pt.png\" alt=\"Change Expanded to Standard Form Game\">\r\n\t\t<\/div>\r\n\t\r\n\t\t<div class=\"game-card-container-inner\">\r\n\t\t\t<div class=\"game-card-container-inner-name\">Change Expanded to Standard Form Game<\/div>\r\n\t\t\t<span class=\"game-card-container-inner-cta\">Play<\/span>\r\n\t\t<\/div>\r\n\t<\/a>\r\n<\/div><div class=\"game-card-container-outer\">\r\n\t<a href=\"https:\/\/www.splashlearn.com\/s\/math-games\/change-to-standard-form\" data-vars-ga-category=\"splashlearn_vocab\" data-vars-ga-action=\"games_recommendations\" data-vars-ga-label=\"post_widget\">\r\n\t\t<div class=\"game-card-container-inner-block\">\r\n\t\t\t<img decoding=\"async\" class=\"game-card-container-inner-img\" src=\"https:\/\/cdn.splashmath.com\/curriculum_uploads\/images\/playables\/place_value_write_in_word_5d_pt.png\" alt=\"Change to Standard Form Game\">\r\n\t\t<\/div>\r\n\t\r\n\t\t<div class=\"game-card-container-inner\">\r\n\t\t\t<div class=\"game-card-container-inner-name\">Change to Standard Form Game<\/div>\r\n\t\t\t<span class=\"game-card-container-inner-cta\">Play<\/span>\r\n\t\t<\/div>\r\n\t<\/a>\r\n<\/div><\/div><p class=\"recommended-games-container-desc\"><a href=\"https:\/\/www.splashlearn.com\/games\">More Games<\/a><\/p><button class=\"scroll-right-arrow\"><\/button><\/div><script type=\"text\/javascript\">\n        document.addEventListener(\"DOMContentLoaded\", function() {\n            const container = document.querySelector(\"#recommended-games-container-id\");\n            const slidesContainer = 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});\n    <\/script><h2 class=\"wp-block-heading\" id=\"1-formula-of-area-of-triangle-in-determinant-form\">Formula of Area of Triangle in Determinant Form<\/h2>\n\n\n\n<p>Normally, the area of a triangle is calculated using the formula $\\frac{1}{2} \\times b \\times h, where b is the base and h is height of the triangle.&nbsp;<\/p>\n\n\n\n<p>Some cases, however, use a different formula for determining the triangle\u2019s area where the height is not given. The vertices of the triangle are employed for the evaluation of the area using the following determinant formula.<\/p>\n\n\n\n<p>Suppose a triangle \u0394PQR has vertices P(x<sub>1<\/sub>, y<sub>1<\/sub>), Q(x<sub>2<\/sub>, y<sub>2<\/sub>), and R(x<sub>3<\/sub>, y<sub>3<\/sub>).&nbsp;<\/p>\n\n\n\n<p>The area of \u0394PQR is given by<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"620\" height=\"308\" src=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/11\/the-area-of-a-triangle-using-determinant.png\" alt=\"The area of a triangle using determinant\" class=\"wp-image-36243\" title=\"The area of a triangle using determinant\" srcset=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/11\/the-area-of-a-triangle-using-determinant.png 620w, https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/11\/the-area-of-a-triangle-using-determinant-300x149.png 300w\" sizes=\"auto, (max-width: 620px) 100vw, 620px\" \/><\/figure>\n\n\n\n<p>Solving the determinant, we get<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"620\" height=\"211\" src=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/11\/simplified-determinant-formula-for-the-area-of-a-triangle.png\" alt=\"Simplified determinant formula for the area of a triangle\" class=\"wp-image-36244\" title=\"Simplified determinant formula for the area of a triangle\" srcset=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/11\/simplified-determinant-formula-for-the-area-of-a-triangle.png 620w, https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/11\/simplified-determinant-formula-for-the-area-of-a-triangle-300x102.png 300w\" sizes=\"auto, (max-width: 620px) 100vw, 620px\" \/><\/figure>\n\n\n\n<div id=\"recommended-worksheets-container-id\" class=\"recommended-games-container\"><h4 class=\"recommended-games-container-headline\">Recommended Worksheets<\/h4><div class=\"recommended-games-container-slides\"><div class=\"worksheet-card-container-outer\">\r\n\t<a href=\"https:\/\/www.splashlearn.com\/s\/math-worksheets\/add-fractions-using-area-models\" data-vars-ga-category=\"splashlearn_vocab\" data-vars-ga-action=\"worksheets_recommendations\" data-vars-ga-label=\"post_widget\">\r\n\t    <div class=\"worksheet-card-container-inner-block\">\r\n\t        <img decoding=\"async\" class=\"worksheet-card-container-inner-img\" src=\"https:\/\/cdn.splashmath.com\/cms_assets\/s\/math-worksheets\/add-fractions-using-area-models.jpeg\" alt=\"Add Fractions using Area Models Worksheet\">\r\n\t    <\/div>\r\n\t\t<div class=\"worksheet-card-container-inner\" >\r\n\t\t<\/div><\/a>\r\n<\/div><div class=\"worksheet-card-container-outer\">\r\n\t<a href=\"https:\/\/www.splashlearn.com\/s\/math-worksheets\/add-like-fractions-using-area-models\" data-vars-ga-category=\"splashlearn_vocab\" data-vars-ga-action=\"worksheets_recommendations\" data-vars-ga-label=\"post_widget\">\r\n\t    <div class=\"worksheet-card-container-inner-block\">\r\n\t        <img decoding=\"async\" class=\"worksheet-card-container-inner-img\" src=\"https:\/\/cdn.splashmath.com\/cms_assets\/s\/math-worksheets\/add-like-fractions-using-area-models.jpeg\" alt=\"Add Like Fractions using Area Models Worksheet\">\r\n\t    <\/div>\r\n\t\t<div class=\"worksheet-card-container-inner\" >\r\n\t\t<\/div><\/a>\r\n<\/div><div class=\"worksheet-card-container-outer\">\r\n\t<a href=\"https:\/\/www.splashlearn.com\/s\/math-worksheets\/add-mixed-numbers-and-fractions-using-area-models\" data-vars-ga-category=\"splashlearn_vocab\" data-vars-ga-action=\"worksheets_recommendations\" data-vars-ga-label=\"post_widget\">\r\n\t    <div class=\"worksheet-card-container-inner-block\">\r\n\t        <img decoding=\"async\" class=\"worksheet-card-container-inner-img\" src=\"https:\/\/cdn.splashmath.com\/cms_assets\/s\/math-worksheets\/add-mixed-numbers-and-fractions-using-area-models.jpeg\" alt=\"Add Mixed Numbers and Fractions using Area Models Worksheet\">\r\n\t    <\/div>\r\n\t\t<div class=\"worksheet-card-container-inner\" >\r\n\t\t<\/div><\/a>\r\n<\/div><div class=\"worksheet-card-container-outer\">\r\n\t<a href=\"https:\/\/www.splashlearn.com\/s\/math-worksheets\/color-animals-and-trace-word-forms-within-10\" data-vars-ga-category=\"splashlearn_vocab\" data-vars-ga-action=\"worksheets_recommendations\" data-vars-ga-label=\"post_widget\">\r\n\t    <div class=\"worksheet-card-container-inner-block\">\r\n\t        <img decoding=\"async\" class=\"worksheet-card-container-inner-img\" src=\"https:\/\/cdn.splashmath.com\/cms_assets\/s\/math-worksheets\/color-animals-and-trace-word-forms-within-10.jpeg\" alt=\"Color Animals and Trace Word Forms (Within 10)\">\r\n\t    <\/div>\r\n\t\t<div class=\"worksheet-card-container-inner\" >\r\n\t\t<\/div><\/a>\r\n<\/div><div class=\"worksheet-card-container-outer\">\r\n\t<a href=\"https:\/\/www.splashlearn.com\/s\/math-worksheets\/color-animals-and-trace-word-forms-within-5\" data-vars-ga-category=\"splashlearn_vocab\" data-vars-ga-action=\"worksheets_recommendations\" data-vars-ga-label=\"post_widget\">\r\n\t    <div class=\"worksheet-card-container-inner-block\">\r\n\t        <img decoding=\"async\" class=\"worksheet-card-container-inner-img\" src=\"https:\/\/cdn.splashmath.com\/cms_assets\/s\/math-worksheets\/color-animals-and-trace-word-forms-within-5.jpeg\" alt=\"Color Animals and Trace Word Forms (Within 5)\">\r\n\t    <\/div>\r\n\t\t<div class=\"worksheet-card-container-inner\" >\r\n\t\t<\/div><\/a>\r\n<\/div><div class=\"worksheet-card-container-outer\">\r\n\t<a href=\"https:\/\/www.splashlearn.com\/s\/math-worksheets\/color-birds-and-trace-word-forms-within-10\" data-vars-ga-category=\"splashlearn_vocab\" data-vars-ga-action=\"worksheets_recommendations\" 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slidesContainer.scrollWidth - slidesContainer.clientWidth;\n                if ((slidesContainer.scrollLeft + 10) >= maxScrollLeft) {\n                    scrollRightArrow.style.display = \"none\"; \/\/ Hide the arrow if fully scrolled\n                } else {\n                    scrollRightArrow.style.display = \"block\"; \/\/ Show the arrow if not fully scrolled\n                }\n            }\n\n            scrollRightArrow.addEventListener(\"click\", function() {\n                const scrollAmount = 300; \/\/ Adjust based on the container's width and your needs\n                slidesContainer.scrollLeft += scrollAmount;\n                setTimeout(checkScrollPosition, 100); \/\/ Delay to allow scroll update\n            });\n\n            adjustContainerStyles();\n            checkScrollPosition();\n            slidesContainer.addEventListener(\"scroll\", checkScrollPosition);\n        });\n    <\/script><h2 class=\"wp-block-heading\" id=\"2-how-to-determine-the-area-of-triangle-in-determinant-form\">How to Determine the Area of Triangle in Determinant Form<\/h2>\n\n\n\n<p>Now that we know the formula to evaluate the area of triangle in determinant form, we will solve a few examples to understand its application.&nbsp;<\/p>\n\n\n\n<p>A determinant value can be both positive or negative. However, area can never be negative. So, we take the absolute value of the result.<\/p>\n\n\n\n<p><strong>Example: <\/strong>Suppose the vertices are P(-1, 2), Q(3, 1), and R(2, 5). So, if we want to determine the area of triangle in determinant form, we will use the above-mentioned formula.<\/p>\n\n\n\n<p>Area $= \\frac{1}{2} \\times \\left[x_{1} (y_{2} &#8211; y_{3}) + x_{2} (y_{3} &#8211; y_{1}) + x_{3} (y_{1} &#8211; y_{2})\\right]$<\/p>\n\n\n\n<p>Here, we know that the coordinates of vertices are P(x<sub>1<\/sub>, y<sub>1<\/sub>), Q(x<sub>2<\/sub>, y<sub>2<\/sub>), and R(x<sub>3<\/sub>, y<sub>3<\/sub>).<\/p>\n\n\n\n<p>x<sub>1<\/sub>= -1, y<sub>1<\/sub>= 2<\/p>\n\n\n\n<p>x<sub>2<\/sub>= 3, y<sub>2<\/sub>= 1<\/p>\n\n\n\n<p>x<sub>3<\/sub>= 2, y<sub>3<\/sub>= 5<\/p>\n\n\n\n<p>Putting the values in the formula, we get<\/p>\n\n\n\n<p>A $= (\\frac{1}{2}) \\left[(-1) (1 &#8211; 5) + 3 (5 &#8211; 2) + 2 (2 &#8211; 1)\\right]$<\/p>\n\n\n\n<p>A $= \\frac{1}{2} \\times 15$<\/p>\n\n\n\n<p>A $= \\frac{15}{2}$ square units<\/p>\n\n\n\n<h2 class=\"wp-block-heading\" id=\"3-facts-about-area-of-triangle-in-determinant-form\">Facts about Area of Triangle in Determinant Form<\/h2>\n\n\n\n<div style=\"color:#0369a1;background-color:#e0f2fe\" class=\"wp-block-roelmagdaleno-callout-block has-text-color has-background is-layout-flex wp-container-roelmagdaleno-callout-block-is-layout-8cf370e7 wp-block-roelmagdaleno-callout-block-is-layout-flex\"><div>\n<ul class=\"wp-block-list\">\n<li>For three collinear points, we get a straight line and the determinant becomes zero.<\/li>\n\n\n\n<li>If the area of the triangle is 0, the three points are collinear.<\/li>\n\n\n\n<li>Area cannot be negative. Thus, if the determinant comes out to be negative, consider the positive value only.<\/li>\n\n\n\n<li>If the area of a triangle is given and we have to find a missing coordinate of a vertex, we consider both positive and negative values of the determinant.<\/li>\n<\/ul>\n<\/div><\/div>\n\n\n\n<h2 class=\"wp-block-heading\" id=\"4-conclusion\">Conclusion<\/h2>\n\n\n\n<p>In this article, we delved into the concept of finding the area of a triangle using the determinant form, a powerful method in linear algebra. We learned how determinants are used to find the area of a triangle, the formula and examples. To reinforce our knowledge, let&#8217;s engage in solving examples and attempting MCQs for better comprehension.&nbsp;<\/p>\n\n\n\n<h2 class=\"wp-block-heading\" id=\"5-solved-examples-on-area-of-triangle-in-determinant-form\">Solved Examples on Area of Triangle in Determinant Form<\/h2>\n\n\n\n<p><strong>1. The three vertices of \u25b5GHI are G(<\/strong><strong>&#8211;<\/strong><strong>1, 1), H(3, 4), and I(2, <\/strong><strong>&#8211;<\/strong><strong>1). How can we find the area of this triangle?<\/strong><\/p>\n\n\n\n<p><strong>Solution:<\/strong><\/p>\n\n\n\n<p>In a case where we just have the vertices given, we can find the area by using the determinant formula.<\/p>\n\n\n\n<p>x<sub>1 <\/sub>= <strong>&#8211;<\/strong>1, y<sub>1 <\/sub>= 1<\/p>\n\n\n\n<p>x<sub>2 <\/sub>= 3, y<sub>2 <\/sub>= 4<\/p>\n\n\n\n<p>x<sub>3 <\/sub>= 2, y<sub>3 <\/sub>= -1<\/p>\n\n\n\n<p>So, let us use the determinant formula.<\/p>\n\n\n\n<p>Area $= \\frac{1}{2} \\times \\left[x_{1} (y_{2} &#8211; y_{3}) + x_{2} (y_{3} &#8211; y_{1}) + x_{3} (y_{1} &#8211; y_{2})\\right]$<\/p>\n\n\n\n<p>Putting the values of the vertices in the formula, we get<\/p>\n\n\n\n<p>A $= \\frac{1}{2} \\times \\left[(-1) (4 &#8211; (-1)) + 3 (-1 &#8211; 1) + 2 (1 &#8211; 4)\\right]$<\/p>\n\n\n\n<p>A $= \\frac{1}{2} \\times \\left[-5 &#8211; 6 &#8211; 6\\right]$<\/p>\n\n\n\n<p>A $=&nbsp; \\frac{-17}{2}$ sq units<\/p>\n\n\n\n<p>Therefore, the area of the triangle GHI is 3.5 sq units.<\/p>\n\n\n\n<p><strong>2. Use a determinant to find the area of the triangle with the given vertices: A(2, 4), B(5, 6), and C(1, 3).&nbsp;<\/strong><\/p>\n\n\n\n<p><strong>Solution:<\/strong><\/p>\n\n\n\n<p>x<sub>1 <\/sub>= 2, y<sub>1 <\/sub>= 4<\/p>\n\n\n\n<p>x<sub>2 <\/sub>= 5, y<sub>2 <\/sub>= 6<\/p>\n\n\n\n<p>x<sub>3 <\/sub>= 1, y<sub>3 <\/sub>= 3<\/p>\n\n\n\n<p>So, let us use the determinant formula.<\/p>\n\n\n\n<p>Area $= \\frac{1}{2} \\times \\left[x_{1} (y_{2} &#8211; y_{3}) + x_{2} (y_{3} &#8211; y_{1}) + x_{3} (y_{1} &#8211; y_{2})\\right]$<\/p>\n\n\n\n<p>Putting the values in the formula, we get<\/p>\n\n\n\n<p>Area $= \\frac{1}{2} \\times \\left[2 (6 &#8211; 3) + 5 (3 &#8211; 4) + 1 (4 -6)\\right]$<\/p>\n\n\n\n<p>Area $= \\frac{1}{2} \\times |&nbsp; -1 |&nbsp;$<\/p>\n\n\n\n<p>Area = 0.5 square unit<\/p>\n\n\n\n<p>Therefore, the area of the triangle ABC is 0.5 square unit.<\/p>\n\n\n\n<p><strong>3. The vertices of a triangle are given as P(0, 0), Q(2, 4), and R(5, 1). What would be the area of this triangle?<\/strong><\/p>\n\n\n\n<p><strong>Solution:<\/strong><\/p>\n\n\n\n<p>x<sub>1<\/sub>= 0, y<sub>1<\/sub>= 0<\/p>\n\n\n\n<p>x<sub>2<\/sub>= 2, y<sub>2<\/sub>= 4<\/p>\n\n\n\n<p>x<sub>3<\/sub>= 5, y<sub>3<\/sub>= 1<\/p>\n\n\n\n<p>A $= \\frac{1}{2} \\times \\left[x_{1} (y_{2} &#8211; y_{3}) + x_{2} (y_{3} &#8211; y_{1}) + x_{3} (y_{1} &#8211; y_{2})\\right]$<\/p>\n\n\n\n<p>Putting the values of the vertices in the formula, we get<\/p>\n\n\n\n<p>A $= (\\frac{1}{2}) \\times \\left[0 (4 &#8211; 1) + 2 (1 &#8211; 0) + 5 (0 &#8211; 4)\\right]$<\/p>\n\n\n\n<p>A $=&nbsp;(\\frac{1}{2}) \\times |-18|$<\/p>\n\n\n\n<p>A = 9<\/p>\n\n\n\n<h2 class=\"wp-block-heading\" id=\"6-practice-problems-of-area-of-triangle-in-determinant-form\">Practice Problems of Area of Triangle in Determinant Form<\/h2>\n\n\n\n<div class=\"spq_wrapper\"><h2 style=\"display:none;\">Area of Triangle in Determinant Form - Definition, Examples<\/h2><p style=\"display:none;\">Attend this quiz & Test your knowledge.<\/p><div class=\"spq_question_wrapper\" data-answer=\"0\"><span class=\"spq_question_header\"><span class=\"sqp_question_number\">1<\/span><h3 class=\"sqp_question_text\">Which is the correct formula for the area of a triangle using the determinant method?<\/h3><\/span><div class=\"spq_answer_block\" data-value=\"0\">A $= \\frac{1}{2} \\times \\left[x_{1} (y_{2} - y_{3}) + x_{2} (y_{3} - y_{1}) + x_{3} (y_{1} - y_{2})\\right]$<\/div><div class=\"spq_answer_block\" data-value=\"1\">A $= \\frac{1}{2} \\times \\left[x_{1} (y_{2} - y_{3}) - x_{2} (y_{3} - y_{1}) + x_{3} (y_{1} - y_{2})\\right]$<\/div><div class=\"spq_answer_block\" data-value=\"2\">A $= \\frac{1}{2} \\times \\left[x_{1} (y_{2} - y_{3}) - x_{2} (y_{3} - y_{1}) - x_{3} (y_{1} - y_{2})\\right]$<\/div><div class=\"spq_answer_block\" data-value=\"3\">A $= \\frac{1}{2} \\times \\left[x_{1} (y_{2} + y_{3}) - x_{2} (y_{3} - y_{1}) - x_{3} (y_{1} + y_{2})\\right]$<\/div><div class=\"sqp_question_hint\"><div class=\"sqp_question_hint__header\"><span class=\"spq_correct\">Correct<\/span><span class=\"spq_incorrect\">Incorrect<\/span><\/div><div class=\"sqp_question_hint__content\"><span>Correct answer is: A $= \\frac{1}{2} \\times \\left[x_{1} (y_{2} - y_{3}) + x_{2} (y_{3} - y_{1}) + x_{3} (y_{1} - y_{2})\\right]$<br\/>If the coordinates of the vertices of a triangle are $(x_{1}, y_{1}), (x_{2}, y_{2})$, and $(x_{3}, y_{3})$, the area is given by<br>\r\nA $= \\frac{1}{2} \\times \\left[x_{1} (y_{2} - y_{3}) + x_{2} (y_{3} - y_{1}) + x_{3} (y_{1} - y_{2})\\right]$.<\/span><\/div><\/div><\/div><div class=\"spq_question_wrapper\" data-answer=\"1\"><span class=\"spq_question_header\"><span class=\"sqp_question_number\">2<\/span><h3 class=\"sqp_question_text\">Consider a triangle whose vertices are located at (-3, 1), (4, 3), and (-1, 5). Using the determinant method, calculate the area of this triangle.<\/h3><\/span><div class=\"spq_answer_block\" data-value=\"0\">24 square units<\/div><div class=\"spq_answer_block\" data-value=\"1\">12 square units<\/div><div class=\"spq_answer_block\" data-value=\"2\">6 square units<\/div><div class=\"spq_answer_block\" data-value=\"3\">9 square units<\/div><div class=\"sqp_question_hint\"><div class=\"sqp_question_hint__header\"><span class=\"spq_correct\">Correct<\/span><span class=\"spq_incorrect\">Incorrect<\/span><\/div><div class=\"sqp_question_hint__content\"><span>Correct answer is: 12 square units<br\/>A $= \\frac{1}{2} \\times \\left[x_{1} (y_{2} - y_{3}) + x_{2} (y_{3} - y_{1}) + x_{3} (y_{1} - y_{2})\\right]$<br>\r\nA $= \\frac{1}{2} \\times \\left[(-3) (3 - 5) + 4 (5 - 1) + (-1) (1 - 3)\\right]$<br>\r\nA $= \\frac{1}{2} \\times \\left[6 + 16 + 2\\right]$<br>\r\nA $= 12 square units<\/span><\/div><\/div><\/div><div class=\"spq_question_wrapper\" data-answer=\"0\"><span class=\"spq_question_header\"><span class=\"sqp_question_number\">3<\/span><h3 class=\"sqp_question_text\">Area of the triangle ABC is 0. It means that<\/h3><\/span><div class=\"spq_answer_block\" data-value=\"0\">A, B, C are collinear.<\/div><div class=\"spq_answer_block\" data-value=\"1\">A, B, C are non-collinear.<\/div><div class=\"spq_answer_block\" data-value=\"2\">A, B, C have negative coordinates.<\/div><div class=\"spq_answer_block\" data-value=\"3\">A, B, C have positive coordinates<\/div><div class=\"sqp_question_hint\"><div class=\"sqp_question_hint__header\"><span class=\"spq_correct\">Correct<\/span><span class=\"spq_incorrect\">Incorrect<\/span><\/div><div class=\"sqp_question_hint__content\"><span>Correct answer is: A, B, C are collinear.<br\/>If the area of a triangle is 0, it means that the vertices of the triangle are collinear.<\/span><\/div><\/div><\/div><\/div>  <script type=\"application\/ld+json\">{\n        \"@context\": \"https:\/\/schema.org\/\", \n        \"@type\": \"Quiz\", \n        \"typicalAgeRange\": \"3-11\",\n        \"educationalLevel\":  \"beginner\",\n        \"assesses\" : \"Attend this quiz & Test your knowledge.\",\n        \"educationalAlignment\": [\n              {\n                \"@type\": \"AlignmentObject\",\n                \"alignmentType\": \"educationalSubject\",\n                \"targetName\": \"Math\"\n              }] ,\n        \"name\": \"Area of Triangle in Determinant Form - 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y_{3}) - x_{2} (y_{3} - y_{1}) + x_{3} (y_{1} - y_{2})\\\\right]$$\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"If the coordinates of the vertices of a triangle are $$(x_{1}, y_{1}), (x_{2}, y_{2})$$, and $$(x_{3}, y_{3})$$, the area is given by<br>\r\nA $$= \\\\frac{1}{2} \\\\times \\\\left[x_{1} (y_{2} - y_{3}) + x_{2} (y_{3} - y_{1}) + x_{3} (y_{1} - y_{2})\\\\right]$$.\"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 2,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"A $$= \\\\frac{1}{2} \\\\times \\\\left[x_{1} (y_{2} - y_{3}) - x_{2} (y_{3} - y_{1}) - x_{3} (y_{1} - y_{2})\\\\right]$$\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"If the coordinates of the vertices of a triangle are $$(x_{1}, y_{1}), (x_{2}, y_{2})$$, and $$(x_{3}, y_{3})$$, the area is given by<br>\r\nA $$= \\\\frac{1}{2} \\\\times \\\\left[x_{1} (y_{2} - y_{3}) + x_{2} (y_{3} - y_{1}) + x_{3} (y_{1} - y_{2})\\\\right]$$.\"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 3,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"A $$= \\\\frac{1}{2} \\\\times \\\\left[x_{1} (y_{2} + y_{3}) - x_{2} (y_{3} - y_{1}) - x_{3} (y_{1} + y_{2})\\\\right]$$\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"If the coordinates of the vertices of a triangle are $$(x_{1}, y_{1}), (x_{2}, y_{2})$$, and $$(x_{3}, y_{3})$$, the area is given by<br>\r\nA $$= \\\\frac{1}{2} \\\\times \\\\left[x_{1} (y_{2} - y_{3}) + x_{2} (y_{3} - y_{1}) + x_{3} (y_{1} - y_{2})\\\\right]$$.\"\n                                    }\n                                }],\n                    \"acceptedAnswer\": {\n                      \"@type\": \"Answer\",\n                      \"position\": 0,\n                      \"encodingFormat\": \"text\/html\",\n                      \"text\": \"A $$= \\\\frac{1}{2} \\\\times \\\\left[x_{1} (y_{2} - y_{3}) + x_{2} (y_{3} - y_{1}) + x_{3} (y_{1} - y_{2})\\\\right]$$\",\n                      \"comment\": {\n                          \"@type\": \"Comment\",\n                          \"text\": \"If the coordinates of the vertices of a triangle are $$(x_{1}, y_{1}), (x_{2}, y_{2})$$, and $$(x_{3}, y_{3})$$, the area is given by<br>\r\nA $$= \\\\frac{1}{2} \\\\times \\\\left[x_{1} (y_{2} - y_{3}) + x_{2} (y_{3} - y_{1}) + x_{3} (y_{1} - y_{2})\\\\right]$$.\"\n                        },\n                      \"answerExplanation\": {\n                        \"@type\": \"Comment\",\n                        \"text\": \"If the coordinates of the vertices of a triangle are $$(x_{1}, y_{1}), (x_{2}, y_{2})$$, and $$(x_{3}, y_{3})$$, the area is given by<br>\r\nA $$= \\\\frac{1}{2} \\\\times \\\\left[x_{1} (y_{2} - y_{3}) + x_{2} (y_{3} - y_{1}) + x_{3} (y_{1} - y_{2})\\\\right]$$.\"\n                      }\n                    } \n\n                    },{\n                    \"@type\": \"Question\",   \n                    \"eduQuestionType\": \"Multiple choice\",\n                    \"learningResourceType\": \"Practice problem\",\n                    \"name\": \"Consider a triangle whose vertices are located at (-3, 1), (4, 3), and (-1, 5). Using the determinant method, calculate the area of this triangle.\",\n                    \"text\": \"Consider a triangle whose vertices are located at (-3, 1), (4, 3), and (-1, 5). Using the determinant method, calculate the area of this triangle.\",\n                    \"comment\": {\n                      \"@type\": \"Comment\",\n                      \"text\": \"A $$= \\\\frac{1}{2} \\\\times \\\\left[x_{1} (y_{2} - y_{3}) + x_{2} (y_{3} - y_{1}) + x_{3} (y_{1} - y_{2})\\\\right]$$<br>\r\nA $$= \\\\frac{1}{2} \\\\times \\\\left[(-3) (3 - 5) + 4 (5 - 1) + (-1) (1 - 3)\\\\right]$$<br>\r\nA $$= \\\\frac{1}{2} \\\\times \\\\left[6 + 16 + 2\\\\right]$$<br>\r\nA $$= 12 square units\"\n                    },\n                    \"encodingFormat\": \"text\/html\",\n                    \"suggestedAnswer\": [ {\n                                \"@type\": \"Answer\",\n                                \"position\": 0,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"24 square units\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"A $$= \\\\frac{1}{2} \\\\times \\\\left[x_{1} (y_{2} - y_{3}) + x_{2} (y_{3} - y_{1}) + x_{3} (y_{1} - y_{2})\\\\right]$$<br>\r\nA $$= \\\\frac{1}{2} \\\\times \\\\left[(-3) (3 - 5) + 4 (5 - 1) + (-1) (1 - 3)\\\\right]$$<br>\r\nA $$= \\\\frac{1}{2} \\\\times \\\\left[6 + 16 + 2\\\\right]$$<br>\r\nA $$= 12 square units\"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 2,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"6 square units\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"A $$= \\\\frac{1}{2} \\\\times \\\\left[x_{1} (y_{2} - y_{3}) + x_{2} (y_{3} - y_{1}) + x_{3} (y_{1} - y_{2})\\\\right]$$<br>\r\nA $$= \\\\frac{1}{2} \\\\times \\\\left[(-3) (3 - 5) + 4 (5 - 1) + (-1) (1 - 3)\\\\right]$$<br>\r\nA $$= \\\\frac{1}{2} \\\\times \\\\left[6 + 16 + 2\\\\right]$$<br>\r\nA $$= 12 square units\"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 3,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"9 square units\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"A $$= \\\\frac{1}{2} \\\\times \\\\left[x_{1} (y_{2} - y_{3}) + x_{2} (y_{3} - y_{1}) + x_{3} (y_{1} - y_{2})\\\\right]$$<br>\r\nA $$= \\\\frac{1}{2} \\\\times \\\\left[(-3) (3 - 5) + 4 (5 - 1) + (-1) (1 - 3)\\\\right]$$<br>\r\nA $$= \\\\frac{1}{2} \\\\times \\\\left[6 + 16 + 2\\\\right]$$<br>\r\nA $$= 12 square units\"\n                                    }\n                                }],\n                    \"acceptedAnswer\": {\n                      \"@type\": \"Answer\",\n                      \"position\": 1,\n                      \"encodingFormat\": \"text\/html\",\n                      \"text\": \"12 square units\",\n                      \"comment\": {\n                          \"@type\": \"Comment\",\n                          \"text\": \"A $$= \\\\frac{1}{2} \\\\times \\\\left[x_{1} (y_{2} - y_{3}) + x_{2} (y_{3} - y_{1}) + x_{3} (y_{1} - y_{2})\\\\right]$$<br>\r\nA $$= \\\\frac{1}{2} \\\\times \\\\left[(-3) (3 - 5) + 4 (5 - 1) + (-1) (1 - 3)\\\\right]$$<br>\r\nA $$= \\\\frac{1}{2} \\\\times \\\\left[6 + 16 + 2\\\\right]$$<br>\r\nA $$= 12 square units\"\n                        },\n                      \"answerExplanation\": {\n                        \"@type\": \"Comment\",\n                        \"text\": \"A $$= \\\\frac{1}{2} \\\\times \\\\left[x_{1} (y_{2} - y_{3}) + x_{2} (y_{3} - y_{1}) + x_{3} (y_{1} - y_{2})\\\\right]$$<br>\r\nA $$= \\\\frac{1}{2} \\\\times \\\\left[(-3) (3 - 5) + 4 (5 - 1) + (-1) (1 - 3)\\\\right]$$<br>\r\nA $$= \\\\frac{1}{2} \\\\times \\\\left[6 + 16 + 2\\\\right]$$<br>\r\nA $$= 12 square units\"\n                      }\n                    } \n\n                    },{\n                    \"@type\": \"Question\",   \n                    \"eduQuestionType\": \"Multiple choice\",\n                    \"learningResourceType\": \"Practice problem\",\n                    \"name\": \"Area of the triangle ABC is 0. It means that\",\n                    \"text\": \"Area of the triangle ABC is 0. It means that\",\n                    \"comment\": {\n                      \"@type\": \"Comment\",\n                      \"text\": \"If the area of a triangle is 0, it means that the vertices of the triangle are collinear.\"\n                    },\n                    \"encodingFormat\": \"text\/html\",\n                    \"suggestedAnswer\": [ {\n                                \"@type\": \"Answer\",\n                                \"position\": 1,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"A, B, C are non-collinear.\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"If the area of a triangle is 0, it means that the vertices of the triangle are collinear.\"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 2,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"A, B, C have negative coordinates.\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"If the area of a triangle is 0, it means that the vertices of the triangle are collinear.\"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 3,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"A, B, C have positive coordinates\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"If the area of a triangle is 0, it means that the vertices of the triangle are collinear.\"\n                                    }\n                                }],\n                    \"acceptedAnswer\": {\n                      \"@type\": \"Answer\",\n                      \"position\": 0,\n                      \"encodingFormat\": \"text\/html\",\n                      \"text\": \"A, B, C are collinear.\",\n                      \"comment\": {\n                          \"@type\": \"Comment\",\n                          \"text\": \"If the area of a triangle is 0, it means that the vertices of the triangle are collinear.\"\n                        },\n                      \"answerExplanation\": {\n                        \"@type\": \"Comment\",\n                        \"text\": \"If the area of a triangle is 0, it means that the vertices of the triangle are collinear.\"\n                      }\n                    } \n\n                    }]}<\/script>\n\n\n\n<h2 class=\"wp-block-heading\" id=\"7-frequently-asked-questions-about-the-area-of-triangle-in-determinant-form\">Frequently Asked Questions about the Area of Triangle in Determinant Form<\/h2>\n\n\n<div class=\"wp-block-ub-content-toggle\" id=\"ub-content-toggle-e6dbc55c-baa4-4759-ba16-0b5a949e5ace\" data-mobilecollapse=\"true\" data-desktopcollapse=\"true\">\n<div class=\"wp-block-ub-content-toggle-accordion\">\n                <div class=\"wp-block-ub-content-toggle-accordion-title-wrap\" aria-expanded=\"false\" aria-controls=\"ub-content-toggle-panel-0-e6dbc55c-baa4-4759-ba16-0b5a949e5ace\" tabindex=\"0\">\n                    <p class=\"wp-block-ub-content-toggle-accordion-title ub-content-toggle-title-e6dbc55c-baa4-4759-ba16-0b5a949e5ace\"><strong>What is the formula for finding the area of a triangle?<\/strong><\/p><div class=\"wp-block-ub-content-toggle-accordion-toggle-wrap right\"><span class=\"wp-block-ub-content-toggle-accordion-state-indicator wp-block-ub-chevron-down\"><\/span>\n                    <\/div><\/div><div role=\"region\" class=\"wp-block-ub-content-toggle-accordion-content-wrap ub-hide\" id=\"ub-content-toggle-panel-0-e6dbc55c-baa4-4759-ba16-0b5a949e5ace\">\n\n<p>Area of a triangle $= \\frac{1}{2} \\times$ base $\\times$ height<\/p>\n\n<\/div><\/div>\n\n<div class=\"wp-block-ub-content-toggle-accordion\">\n                <div class=\"wp-block-ub-content-toggle-accordion-title-wrap\" aria-expanded=\"false\" aria-controls=\"ub-content-toggle-panel-1-e6dbc55c-baa4-4759-ba16-0b5a949e5ace\" tabindex=\"0\">\n                    <p class=\"wp-block-ub-content-toggle-accordion-title ub-content-toggle-title-e6dbc55c-baa4-4759-ba16-0b5a949e5ace\"><strong>Is it possible to calculate the area of any triangle using the determinant method?<\/strong><\/p><div class=\"wp-block-ub-content-toggle-accordion-toggle-wrap right\"><span class=\"wp-block-ub-content-toggle-accordion-state-indicator wp-block-ub-chevron-down\"><\/span>\n                    <\/div><\/div><div role=\"region\" class=\"wp-block-ub-content-toggle-accordion-content-wrap ub-hide\" id=\"ub-content-toggle-panel-1-e6dbc55c-baa4-4759-ba16-0b5a949e5ace\">\n\n<p>Yes, the area of any <a href=\"https:\/\/www.splashlearn.com\/math-vocabulary\/geometry\/triangle\">triangle<\/a> can be found by employing the determinant method if the coordinates of the vertices are known.<\/p>\n\n<\/div><\/div>\n\n<div class=\"wp-block-ub-content-toggle-accordion\">\n                <div class=\"wp-block-ub-content-toggle-accordion-title-wrap\" aria-expanded=\"false\" aria-controls=\"ub-content-toggle-panel-2-e6dbc55c-baa4-4759-ba16-0b5a949e5ace\" tabindex=\"0\">\n                    <p class=\"wp-block-ub-content-toggle-accordion-title ub-content-toggle-title-e6dbc55c-baa4-4759-ba16-0b5a949e5ace\"><strong>What is Heron\u2019s formula for finding the area of a triangle?<\/strong><\/p><div class=\"wp-block-ub-content-toggle-accordion-toggle-wrap right\"><span class=\"wp-block-ub-content-toggle-accordion-state-indicator wp-block-ub-chevron-down\"><\/span>\n                    <\/div><\/div><div role=\"region\" class=\"wp-block-ub-content-toggle-accordion-content-wrap ub-hide\" id=\"ub-content-toggle-panel-2-e6dbc55c-baa4-4759-ba16-0b5a949e5ace\">\n\n<p>Heron\u2019s formula for finding the area of a triangle $= A = \\sqrt{s(s &#8211; a)(s &#8211; b)(s &#8211; c)}$, where s is the semiperimeter of the triangle; a, b, and c are the lengths of the sides.<\/p>\n\n<\/div><\/div>\n<\/div>","protected":false},"excerpt":{"rendered":"<p>What Is the Area of a Triangle in Determinant Form? In coordinate geometry, the area of a triangle in determinant form can be calculated when the coordinates of the vertices of the triangle are provided. Calculating the area of a triangle in determinant form is an important application of determinants. If the vertices of a &#8230; <a title=\"Area of Triangle in Determinant Form &#8211; Definition, Examples\" class=\"read-more\" href=\"https:\/\/www.splashlearn.com\/math-vocabulary\/area-of-triangle-in-determinant-form\" aria-label=\"More on Area of Triangle in Determinant Form &#8211; Definition, Examples\">Read more<\/a><\/p>\n","protected":false},"author":2,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"ub_ctt_via":"","footnotes":""},"categories":[1],"tags":[],"class_list":["post-36233","post","type-post","status-publish","format-standard","hentry","category-all"],"featured_image_src":null,"author_info":{"display_name":"Mithun Jhawar","author_link":"https:\/\/www.splashlearn.com\/math-vocabulary\/author\/mithun-jhawarsplashlearn-com\/"},"acf":[],"aioseo_notices":[],"_links":{"self":[{"href":"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-json\/wp\/v2\/posts\/36233","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-json\/wp\/v2\/users\/2"}],"replies":[{"embeddable":true,"href":"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-json\/wp\/v2\/comments?post=36233"}],"version-history":[{"count":10,"href":"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-json\/wp\/v2\/posts\/36233\/revisions"}],"predecessor-version":[{"id":39981,"href":"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-json\/wp\/v2\/posts\/36233\/revisions\/39981"}],"wp:attachment":[{"href":"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-json\/wp\/v2\/media?parent=36233"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-json\/wp\/v2\/categories?post=36233"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-json\/wp\/v2\/tags?post=36233"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}