{"id":841,"date":"2023-03-13T11:08:14","date_gmt":"2023-03-13T11:08:14","guid":{"rendered":"https:\/\/www.matematikazavsicki.com\/en\/?p=841"},"modified":"2023-03-13T11:08:15","modified_gmt":"2023-03-13T11:08:15","slug":"quadrilateral-without-parallel-sides","status":"publish","type":"post","link":"https:\/\/www.matematikazavsicki.com\/en\/quadrilateral-without-parallel-sides\/","title":{"rendered":"Quadrilateral without parallel sides"},"content":{"rendered":"\n<p>What is that quadrilateral that has no parallel sides? A quadrilateral without parallel sides may or may not have two or three equal sides.<\/p>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full is-resized\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/www.matematikazavsicki.com\/en\/wp-content\/uploads\/2023\/03\/A-quadrilateral-without-parallel-sides.jpg\" alt=\"A quadrilateral without parallel sides\" class=\"wp-image-843\" width=\"375\" height=\"207\" srcset=\"https:\/\/www.matematikazavsicki.com\/en\/wp-content\/uploads\/2023\/03\/A-quadrilateral-without-parallel-sides.jpg 500w, https:\/\/www.matematikazavsicki.com\/en\/wp-content\/uploads\/2023\/03\/A-quadrilateral-without-parallel-sides-300x166.jpg 300w\" sizes=\"auto, (max-width: 375px) 100vw, 375px\" \/><figcaption class=\"wp-element-caption\">Quadrilateral without parallel sides<\/figcaption><\/figure>\n<\/div>\n\n\n<h3 class=\"wp-block-heading\">Perimeter<\/h3>\n\n\n\n<p>The formula for calculating the perimeter of this geometric figure is:<\/p>\n\n\n\n<p>Assuming that all four sides of the quadrilateral are of different lengths, their labels are: a, b, c and d. The sum of the four sides gives us the value for its perimeter.<\/p>\n\n\n\n<p class=\"has-vivid-purple-color has-text-color\">Example number 1: Calculate the perimeter of a quadrilateral with side lengths of 5cm, 7cm, 3cm and 8cm.<\/p>\n\n\n\n<p class=\"has-vivid-purple-color has-text-color\">To determine the perimeter of this quadrilateral, it is sufficient to calculate the sum of all four sides: L= 5cm + 7cm + 3cm +8cm.<\/p>\n\n\n\n<p class=\"has-vivid-purple-color has-text-color\">The perimeter of this quadrilateral is 23 cm.<\/p>\n\n\n\n<h2 class=\"wp-block-heading\">Area of a quadrilateral without parallel sides<\/h2>\n\n\n\n<p>The area of a quadrilateral without parallel sides can only be determined if one of its two diagonals is known. In that situation the quadrilateral is divided into two triangles. In doing so, the area of the triangles is calculated, so that finally their sum gives us the area of the quadrilateral itself.<\/p>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full is-resized\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/www.matematikazavsicki.com\/en\/wp-content\/uploads\/2023\/03\/Formula-for-the-area-of-a-quadrilateral-without-parallel-sides.jpg\" alt=\"Formula for the area of a quadrilateral without parallel sides\" class=\"wp-image-849\" width=\"250\" height=\"77\" srcset=\"https:\/\/www.matematikazavsicki.com\/en\/wp-content\/uploads\/2023\/03\/Formula-for-the-area-of-a-quadrilateral-without-parallel-sides.jpg 500w, https:\/\/www.matematikazavsicki.com\/en\/wp-content\/uploads\/2023\/03\/Formula-for-the-area-of-a-quadrilateral-without-parallel-sides-300x92.jpg 300w\" sizes=\"auto, (max-width: 250px) 100vw, 250px\" \/><\/figure>\n<\/div>\n\n\n<p class=\"has-vivid-purple-color has-text-color\">Example number 2: To determine the area of the quadrilateral shown in the figure below:<\/p>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"362\" height=\"307\" src=\"https:\/\/www.matematikazavsicki.com\/en\/wp-content\/uploads\/2023\/03\/Area-of-a-quadrilateral-without-parallel-sides.jpg\" alt=\"Area of a quadrilateral without parallel sides\" class=\"wp-image-852\" srcset=\"https:\/\/www.matematikazavsicki.com\/en\/wp-content\/uploads\/2023\/03\/Area-of-a-quadrilateral-without-parallel-sides.jpg 362w, https:\/\/www.matematikazavsicki.com\/en\/wp-content\/uploads\/2023\/03\/Area-of-a-quadrilateral-without-parallel-sides-300x254.jpg 300w\" sizes=\"auto, (max-width: 362px) 100vw, 362px\" \/><figcaption class=\"wp-element-caption\">An example of a quadrilateral divided into two triangles by one of its diagonals<\/figcaption><\/figure>\n<\/div>\n\n\n<p>Obviously, the quadrilateral in the figure is combination of two triangles PRQ and PRS. To solve the problem, it is necessary to determine the area of the two triangles. Finally, the sum of the areas of the triangles represents the area of the quadrilateral.<\/p>\n\n\n\n<p>The area of triangles in this situation can be calculated using Heron&#8217;s formula:<\/p>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"500\" height=\"75\" src=\"https:\/\/www.matematikazavsicki.com\/en\/wp-content\/uploads\/2023\/03\/Herons-formula-for-the-area-of-a-triangle.jpg\" alt=\"Heron's formula for the area of a triangle\" class=\"wp-image-856\" srcset=\"https:\/\/www.matematikazavsicki.com\/en\/wp-content\/uploads\/2023\/03\/Herons-formula-for-the-area-of-a-triangle.jpg 500w, https:\/\/www.matematikazavsicki.com\/en\/wp-content\/uploads\/2023\/03\/Herons-formula-for-the-area-of-a-triangle-300x45.jpg 300w\" sizes=\"auto, (max-width: 500px) 100vw, 500px\" \/><figcaption class=\"wp-element-caption\">Heron&#8217;s formula for the area of a triangle<\/figcaption><\/figure>\n<\/div>\n\n\n<p>In the formula, s denotes half of the perimeter of the triangle, and the symbols a, b and c are the sides of the triangle.<\/p>\n\n\n\n<p class=\"has-vivid-purple-color has-text-color\">The whole calculation has the following flow:<\/p>\n\n\n\n<ol class=\"wp-block-list\">\n<li>Calculation of half the perimeter of the PRQ.<\/li>\n\n\n\n<li>Area of PRQ.<\/li>\n\n\n\n<li>Calculation of half the perimeter of the PRS.<\/li>\n\n\n\n<li>Area of PRS<\/li>\n\n\n\n<li>Sum of the areas PRQ and PRS.<\/li>\n<\/ol>\n\n\n\n<p class=\"has-vivid-purple-color has-text-color\">Part One: Half Perimeter Calculation for Triangle PRQ:<\/p>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full is-resized\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/www.matematikazavsicki.com\/en\/wp-content\/uploads\/2023\/03\/S1.jpg\" alt=\"S1\" class=\"wp-image-860\" width=\"375\" height=\"111\" srcset=\"https:\/\/www.matematikazavsicki.com\/en\/wp-content\/uploads\/2023\/03\/S1.jpg 500w, https:\/\/www.matematikazavsicki.com\/en\/wp-content\/uploads\/2023\/03\/S1-300x89.jpg 300w\" sizes=\"auto, (max-width: 375px) 100vw, 375px\" \/><\/figure>\n<\/div>\n\n\n<p class=\"has-vivid-purple-color has-text-color\">The length of the semi-perimeter of the triangle PRQ is 10 cm.<\/p>\n\n\n\n<p class=\"has-vivid-purple-color has-text-color\">Second part: Calculation of the area of the triangle PRQ:<\/p>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"500\" height=\"61\" src=\"https:\/\/www.matematikazavsicki.com\/en\/wp-content\/uploads\/2023\/03\/P1.jpg\" alt=\"P1\" class=\"wp-image-863\" srcset=\"https:\/\/www.matematikazavsicki.com\/en\/wp-content\/uploads\/2023\/03\/P1.jpg 500w, https:\/\/www.matematikazavsicki.com\/en\/wp-content\/uploads\/2023\/03\/P1-300x37.jpg 300w\" sizes=\"auto, (max-width: 500px) 100vw, 500px\" \/><\/figure>\n<\/div>\n\n\n<p class=\"has-vivid-purple-color has-text-color\">from which it follows that:<\/p>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full is-resized\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/www.matematikazavsicki.com\/en\/wp-content\/uploads\/2023\/03\/P1-1.jpg\" alt=\"P1-1\" class=\"wp-image-865\" width=\"182\" height=\"68\"\/><\/figure>\n<\/div>\n\n\n<p class=\"has-vivid-purple-color has-text-color\">The area of triangle PRQ is approximately 17.32 square centimeters.<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Part Three<\/h3>\n\n\n\n<p class=\"has-vivid-purple-color has-text-color\">Part Three: Half Perimeter Calculation for Triangle PRS:<\/p>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full is-resized\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/www.matematikazavsicki.com\/en\/wp-content\/uploads\/2023\/03\/s2.jpg\" alt=\"s2 Semi-perimeter for quadrilateral without parallel sides\" class=\"wp-image-868\" width=\"375\" height=\"104\" srcset=\"https:\/\/www.matematikazavsicki.com\/en\/wp-content\/uploads\/2023\/03\/s2.jpg 500w, https:\/\/www.matematikazavsicki.com\/en\/wp-content\/uploads\/2023\/03\/s2-300x83.jpg 300w\" sizes=\"auto, (max-width: 375px) 100vw, 375px\" \/><\/figure>\n<\/div>\n\n\n<p class=\"has-vivid-purple-color has-text-color\">The length of the semi-perimeter of the triangle PRS is 10.25 cm.<\/p>\n\n\n\n<p class=\"has-vivid-purple-color has-text-color\">Part Four: Calculation of the area of the triangle PRS:<\/p>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"500\" height=\"54\" src=\"https:\/\/www.matematikazavsicki.com\/en\/wp-content\/uploads\/2023\/03\/s2-1.jpg\" alt=\"s2-1\" class=\"wp-image-870\" srcset=\"https:\/\/www.matematikazavsicki.com\/en\/wp-content\/uploads\/2023\/03\/s2-1.jpg 500w, https:\/\/www.matematikazavsicki.com\/en\/wp-content\/uploads\/2023\/03\/s2-1-300x32.jpg 300w\" sizes=\"auto, (max-width: 500px) 100vw, 500px\" \/><\/figure>\n<\/div>\n\n\n<p class=\"has-vivid-purple-color has-text-color\">from which it follows that:<\/p>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full is-resized\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/www.matematikazavsicki.com\/en\/wp-content\/uploads\/2023\/03\/P2-2.jpg\" alt=\"P2-2\" class=\"wp-image-873\" width=\"250\" height=\"71\" srcset=\"https:\/\/www.matematikazavsicki.com\/en\/wp-content\/uploads\/2023\/03\/P2-2.jpg 500w, https:\/\/www.matematikazavsicki.com\/en\/wp-content\/uploads\/2023\/03\/P2-2-300x85.jpg 300w\" sizes=\"auto, (max-width: 250px) 100vw, 250px\" \/><\/figure>\n<\/div>\n\n\n<p class=\"has-vivid-purple-color has-text-color\">The area of triangle PRS is approximately 19.17 square centimeters.<\/p>\n\n\n\n<p class=\"has-vivid-purple-color has-text-color\">Fifth part: Calculation of the sum of the areas of PRQ and PRS.<\/p>\n\n\n\n<p class=\"has-vivid-purple-color has-text-color\">The area of the quadrilateral without parallel sides is approximately 36.49 square centimeters.<\/p>\n\n\n\n<p>If a quadrilateral (without parallel sides) has two adjacent equal sides, it is a deltoid.<\/p>\n\n\n\n<hr class=\"wp-block-separator has-css-opacity\"\/>\n\n\n<form role=\"search\" method=\"get\" action=\"https:\/\/www.matematikazavsicki.com\/en\/\" class=\"wp-block-search__button-outside wp-block-search__text-button wp-block-search\"    ><label class=\"wp-block-search__label\" for=\"wp-block-search__input-1\" >Enter the mathematical term you want to explore!<\/label><div class=\"wp-block-search__inside-wrapper\" ><input class=\"wp-block-search__input\" id=\"wp-block-search__input-1\" placeholder=\"What do you want to study?\" value=\"\" type=\"search\" name=\"s\" required \/><button aria-label=\"Search\" class=\"wp-block-search__button wp-element-button\" type=\"submit\" >Search<\/button><\/div><\/form>\n\n\n<hr class=\"wp-block-separator has-css-opacity\"\/>\n\n\n\n<p>Follow 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A quadrilateral without parallel sides may or may not have two or three equal sides. Perimeter The formula for calculating the [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":880,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[8,3,4,7,12],"tags":[88,68,116,97,87,113,115,114],"class_list":["post-841","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-10th-grade","category-5th-grade","category-6th-grade","category-9th-grade","category-geometry","tag-area","tag-formula","tag-herons-formula","tag-parallel","tag-perimeter","tag-quadrilateral","tag-sides","tag-without"],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v26.5 - https:\/\/yoast.com\/wordpress\/plugins\/seo\/ -->\n<title>Quadrilateral without parallel sides - Math For All<\/title>\n<meta name=\"description\" content=\"What is that quadrilateral that has no parallel sides? 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