{"id":54696,"date":"2024-02-02T13:51:19","date_gmt":"2024-02-02T13:51:19","guid":{"rendered":"https:\/\/mathema.me\/?p=54696"},"modified":"2024-02-02T13:51:21","modified_gmt":"2024-02-02T13:51:21","slug":"how-to-find-the-are","status":"publish","type":"post","link":"https:\/\/mathema.me\/en\/blog\/how-to-find-the-are\/","title":{"rendered":"How to find the area of a triangle, rectangle, circle, and other shapes. All area formulas"},"content":{"rendered":"\n<p>Calculating the area of a figure is a fundamental concept in school geometry. Each specific shape has its own distinct formula. Mathema provides instructions on how to determine the area of a triangle, parallelogram, rhombus, circle, and various other geometric shapes. Keep this article for reference and utilize it as a handy guide for area formulas required in the mathematics section of your standardized exams.<\/p>\n\n\n\n<h2 class=\"wp-block-heading\">Area of a Triangle <\/h2>\n\n\n\n<h3 class=\"wp-block-heading\">How to calculate the area of a triangle? <\/h3>\n\n\n\n<p>To find the area of a triangle, you can use the formula: it&#8217;s half of the base multiplied by the height drawn to that base. Alternatively, you can use Heron&#8217;s formula, which involves finding half of the triangle&#8217;s perimeter.<\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n\\[S=\\frac12ah\\]\n\n\n\n\\[S=\\sqrt{p(p-a)(p-b)(p-c)}\\]\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<ul class=\"wp-block-list\">\n<li>a \u2014 represents one of the sides of a triangle <\/li>\n\n\n\n<li>h \u2014 stands for the height of a triangle <\/li>\n\n\n\n<li>p \u2014 denotes half of the triangle&#8217;s perimeter<\/li>\n<\/ul>\n\n\n\n<h3 class=\"wp-block-heading\">How to find the area of an equilateral triangle?<\/h3>\n\n\n\n<p>In an equilateral triangle, all angles measure 60\u00b0, and all sides have the same length. You can calculate the area of an equilateral triangle using various formulas:<\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n\\[S=\\frac{a^2\\sqrt3}4\\]\n\n\n\n\\[S=\\frac12ah\\]\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<ul class=\"wp-block-list\">\n<li>a \u2014 one of the triangle&#8217;s sides<\/li>\n\n\n\n<li>h \u2014 the triangle&#8217;s height<\/li>\n<\/ul>\n\n\n\n<h3 class=\"wp-block-heading\">How to find the area of an isosceles triangle?<\/h3>\n\n\n\n<p>In an isosceles triangle, two sides have equal lengths, and the third side is referred to as the base. The area of an isosceles triangle is half of the base multiplied by the height.<\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n\\[S=\\frac12ah\\]\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<ul class=\"wp-block-list\">\n<li>a \u2014 represents the base of a triangle<\/li>\n\n\n\n<li>h \u2014 signifies the height of a triangle<\/li>\n<\/ul>\n\n\n\n<h3 class=\"wp-block-heading\">How to find the area of a right triangle?<\/h3>\n\n\n\n<p>In a right triangle, one of the angles measures 90\u00b0. The sides that create this angle are referred to as the legs, and the opposite side is called the hypotenuse. The area of a right triangle is half of the product of its legs.<\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n\\[S=\\frac12ab\\]\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<ul class=\"wp-block-list\">\n<li>a \u2014 the base of a triangle <\/li>\n\n\n\n<li>h \u2014 the height of a triangle<\/li>\n<\/ul>\n\n\n\n<h3 class=\"wp-block-heading\">How to find the area of a right triangle?<\/h3>\n\n\n\n<p>In a right triangle, one of the angles is a 90\u00b0 angle. The sides that create this angle are referred to as the legs, while the opposite side is known as the hypotenuse. To calculate the area of a right triangle, you can use the formula: it&#8217;s half of the product of the lengths of its legs.<\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n\\[S=\\frac12ab\\]\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<ul class=\"wp-block-list\">\n<li>a, b \u2014 the legs<\/li>\n<\/ul>\n\n\n\n<h2 class=\"wp-block-heading\">Area of a Quadrilateral<\/h2>\n\n\n\n<h3 class=\"wp-block-heading\">How to find the area of a square?<\/h3>\n\n\n\n<p>A square is a four-sided shape with all sides equal in length, and all angles measuring 90\u00b0. The formula to determine the area of a square is perhaps the simplest among all geometry formulas; it is equal to the square of its side length.<\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n\\[S=a^2\\]\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<ul class=\"wp-block-list\">\n<li>a \u2014 length of one side of the square<\/li>\n<\/ul>\n\n\n\n<h3 class=\"wp-block-heading\">How to find the area of a rectangle?<\/h3>\n\n\n\n<p>A rectangle is a four-sided shape where adjacent sides form right angles. While a square shares these characteristics, a rectangle is specifically identified by having unequal adjacent sides. The area of a rectangle is calculated by multiplying the lengths of its adjacent sides.<\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n\\[S=ab\\]\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<ul class=\"wp-block-list\">\n<li>a, b \u2014 lengths of the adjacent sides of the rectangle<\/li>\n<\/ul>\n\n\n\n<h3 class=\"wp-block-heading\">How to find the area of a parallelogram?<\/h3>\n\n\n\n<p>A parallelogram is a four-sided shape with opposite sides that are parallel and equal in length. Opposite angles are also equal. The area of a parallelogram is found by multiplying one of its sides by the height drawn to that side. Alternatively, it can be calculated as the product of two adjacent sides, multiplied by the sine of the angle between them.<\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n\\[S=ah\\]\n\n\n\n\\[S=ab\\sin\\gamma\\]\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<ul class=\"wp-block-list\">\n<li>a, b \u2014 lengths of adjacent sides of the parallelogram<\/li>\n\n\n\n<li>\u03b3 \u2014 angle between the adjacent sides of the parallelogram<\/li>\n\n\n\n<li>h \u2014 height of the parallelogram<\/li>\n<\/ul>\n\n\n\n<h3 class=\"wp-block-heading\">How to find the area of a rhombus?<\/h3>\n\n\n\n<p>A rhombus is a parallelogram with all sides equal in length. Several methods exist to determine the area of a rhombus. One approach is to find half of the product of its diagonals. Another method involves calculating the area as the product of a side and the height drawn to that side.<\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n\\[S=\\frac12d_1d_2\\]\n\n\n\n\\[S=ah\\]\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<ul class=\"wp-block-list\">\n<li>d \u2014 lengths of the diagonals of the rhombus<\/li>\n\n\n\n<li>a \u2014 length of a side of the rhombus<\/li>\n\n\n\n<li>h \u2014 height of the rhombus<\/li>\n<\/ul>\n\n\n\n<h3 class=\"wp-block-heading\">How to find the area of a trapezoid?<\/h3>\n\n\n\n<p>A trapezoid is a four-sided shape with two parallel sides and two non-parallel sides. The parallel sides are referred to as the bases of the trapezoid. To find the area of a trapezoid, including an isosceles trapezoid, you take half of the sum of its bases and multiply it by the height.<\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n\\[S=\\frac{a+b}2h\\]\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<ul class=\"wp-block-list\">\n<li>a, b \u2014 lengths of the bases of the trapezoid<\/li>\n\n\n\n<li>h \u2014 height of the trapezoid<\/li>\n<\/ul>\n\n\n\n<h2 class=\"wp-block-heading\">How to find the area of a circle?<\/h2>\n\n\n\n<p>To calculate the area of a circle, you square its radius and multiply it by the mathematical constant \u03c0 (pi).<\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n\\[S=\\pi R^2\\]\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<ul class=\"wp-block-list\">\n<li>R \u2014 radius of the circle<\/li>\n\n\n\n<li>\u03c0 \u2014 Pi, approximately 3.14<\/li>\n<\/ul>\n\n\n\n<h2 class=\"wp-block-heading\">How to find the surface area of a sphere?<\/h2>\n\n\n\n<p>To determine the surface area of a sphere, you square its radius, multiply it by the mathematical constant \u03c0 (pi), and then multiply the result by four.<\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n\\[S=4\\pi R^2\\]\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<ul class=\"wp-block-list\">\n<li>R \u2014 radius of the sphere<\/li>\n\n\n\n<li>\u03c0 \u2014 Pi, approximately 3.14<\/li>\n<\/ul>\n","protected":false},"excerpt":{"rendered":"<p>Calculating the area of a figure is a fundamental concept in school geometry. Each specific shape has its own distinct [&hellip;]<\/p>\n","protected":false},"author":20,"featured_media":54698,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"_acf_changed":false,"_glsr_average":0,"_glsr_ranking":0,"_glsr_reviews":0,"_jetpack_memberships_contains_paid_content":false,"footnotes":""},"categories":[491],"tags":[],"class_list":["post-54696","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-blog"],"acf":[],"jetpack_featured_media_url":"https:\/\/i0.wp.com\/mathema.me\/wp-content\/uploads\/2024\/01\/2.png?fit=1920%2C1200&ssl=1","jetpack_sharing_enabled":true,"_links":{"self":[{"href":"https:\/\/mathema.me\/en\/wp-json\/wp\/v2\/posts\/54696","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/mathema.me\/en\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/mathema.me\/en\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/mathema.me\/en\/wp-json\/wp\/v2\/users\/20"}],"replies":[{"embeddable":true,"href":"https:\/\/mathema.me\/en\/wp-json\/wp\/v2\/comments?post=54696"}],"version-history":[{"count":0,"href":"https:\/\/mathema.me\/en\/wp-json\/wp\/v2\/posts\/54696\/revisions"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/mathema.me\/en\/wp-json\/wp\/v2\/media\/54698"}],"wp:attachment":[{"href":"https:\/\/mathema.me\/en\/wp-json\/wp\/v2\/media?parent=54696"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/mathema.me\/en\/wp-json\/wp\/v2\/categories?post=54696"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/mathema.me\/en\/wp-json\/wp\/v2\/tags?post=54696"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}