{"id":779,"date":"2023-03-10T08:34:57","date_gmt":"2023-03-10T08:34:57","guid":{"rendered":"https:\/\/www.matematikazavsicki.com\/en\/?p=779"},"modified":"2023-03-10T08:34:58","modified_gmt":"2023-03-10T08:34:58","slug":"trapezoid-and-types-of-trapezoids","status":"publish","type":"post","link":"https:\/\/www.matematikazavsicki.com\/en\/trapezoid-and-types-of-trapezoids\/","title":{"rendered":"Trapezoid and types of trapezoids"},"content":{"rendered":"\n<p class=\"wp-block-paragraph\">A trapezoid is a quadrilateral that has one pair of parallel sides. The only sufficient condition for a quadrilateral to be a trapezoid is that it has only one pair of parallel sides.<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Perimeter<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">Labels on the sides of this geometric 2D figure are:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>The longer side of the pair of parallel sides is denoted by a.<\/li>\n\n\n\n<li>The shorter side of the pair of parallel sides is denoted by b.<\/li>\n\n\n\n<li>The sides that are not parallel are indicated by c and d.<\/li>\n<\/ul>\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\/Trapezoid.jpg\" alt=\"Trapezoid\" class=\"wp-image-792\" width=\"375\" height=\"208\" srcset=\"https:\/\/www.matematikazavsicki.com\/en\/wp-content\/uploads\/2023\/03\/Trapezoid.jpg 500w, https:\/\/www.matematikazavsicki.com\/en\/wp-content\/uploads\/2023\/03\/Trapezoid-300x166.jpg 300w\" sizes=\"auto, (max-width: 375px) 100vw, 375px\" \/><figcaption class=\"wp-element-caption\">Trapezoid<\/figcaption><\/figure>\n<\/div>\n\n\n<p class=\"wp-block-paragraph\">The perimeter of is calculated using the formula:<\/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-Perimeter-of-a-Trapezoid.jpg\" alt=\"Formula for Perimeter of a Trapezoid\" class=\"wp-image-794\" width=\"375\" height=\"65\" srcset=\"https:\/\/www.matematikazavsicki.com\/en\/wp-content\/uploads\/2023\/03\/Formula-for-Perimeter-of-a-Trapezoid.jpg 500w, https:\/\/www.matematikazavsicki.com\/en\/wp-content\/uploads\/2023\/03\/Formula-for-Perimeter-of-a-Trapezoid-300x52.jpg 300w\" sizes=\"auto, (max-width: 375px) 100vw, 375px\" \/><\/figure>\n<\/div>\n\n\n<p class=\"has-vivid-purple-color has-text-color wp-block-paragraph\">Example number 1: Calculate the perimeter of a trapezoid whose bases are 15cm and 11cm, if the pair of sides that are not parallel have lengths of 4cm and 4.5cm.<\/p>\n\n\n\n<p class=\"has-vivid-purple-color has-text-color wp-block-paragraph\">To determine the perimeter of the trapezoid from example 1, it is enough to calculate the sum of all its sides: L=15cm+11cm+4.5cm+4cm<\/p>\n\n\n\n<p class=\"has-vivid-purple-color has-text-color wp-block-paragraph\">The perimeter of this geometric figure is 34.5 cm.<\/p>\n\n\n\n<h2 class=\"wp-block-heading\">Area of a trapezoid<\/h2>\n\n\n\n<p class=\"wp-block-paragraph\">The formula for determining the area of a trapezoid is:<\/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-trapezoid.jpg\" alt=\"Formula for the area\" class=\"wp-image-796\" width=\"250\" height=\"127\" srcset=\"https:\/\/www.matematikazavsicki.com\/en\/wp-content\/uploads\/2023\/03\/Formula-for-the-area-of-a-trapezoid.jpg 500w, https:\/\/www.matematikazavsicki.com\/en\/wp-content\/uploads\/2023\/03\/Formula-for-the-area-of-a-trapezoid-300x152.jpg 300w\" sizes=\"auto, (max-width: 250px) 100vw, 250px\" \/><\/figure>\n<\/div>\n\n\n<p class=\"wp-block-paragraph\">In the formula, the symbol h is in use for the height of the trapezoid.<\/p>\n\n\n\n<p class=\"has-vivid-purple-color has-text-color wp-block-paragraph\">Example number 2: Calculate the area of a trapezoid with bases 12cm and 8cm, if its height is 6cm.<\/p>\n\n\n\n<p class=\"has-vivid-purple-color has-text-color wp-block-paragraph\">The calculation for determining the area can proceed as follows:<\/p>\n\n\n\n<ol class=\"wp-block-list\">\n<li>The sum a+b is: 12cm + 8cm = 20cm<\/li>\n\n\n\n<li>Then the sum of a+b in division by 2: 20cm : 2 = 10cm<\/li>\n\n\n\n<li>The result of step 2 is in multiplication by the height.<\/li>\n<\/ol>\n\n\n\n<p class=\"wp-block-paragraph\">Finally, the area of the figure from example number two is 60 square centimeters.<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Isosceles trapezoid<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">Isosceles is the trapezoid in which the length of the pair of non-parallel sides is equal, that is, the length of sides c and d is equal. Due to the equality of the two non-parallel sides, both are c.<\/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\/An-isosceles-trapezoid.jpg\" alt=\"An isosceles trapezoid\" class=\"wp-image-798\" width=\"375\" height=\"206\" srcset=\"https:\/\/www.matematikazavsicki.com\/en\/wp-content\/uploads\/2023\/03\/An-isosceles-trapezoid.jpg 500w, https:\/\/www.matematikazavsicki.com\/en\/wp-content\/uploads\/2023\/03\/An-isosceles-trapezoid-300x164.jpg 300w\" sizes=\"auto, (max-width: 375px) 100vw, 375px\" \/><figcaption class=\"wp-element-caption\">Isosceles<\/figcaption><\/figure>\n<\/div>\n\n\n<p class=\"wp-block-paragraph\">The formulas for calculating the perimeter and area in this variant are identical to the formulas above that apply to any other member of this figure.<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">A rectangular trapezoid<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">A trapezoid is rectangular, which has exactly two right angles of 90 degrees each.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">The formula for calculating the area of the rectangular variant remains in the same form as for the perimeter of any other member of this geometric figure.<\/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-rectangular-trapezoid.jpg\" alt=\"A rectangular trapezoid\" class=\"wp-image-800\" width=\"375\" height=\"216\" srcset=\"https:\/\/www.matematikazavsicki.com\/en\/wp-content\/uploads\/2023\/03\/A-rectangular-trapezoid.jpg 500w, https:\/\/www.matematikazavsicki.com\/en\/wp-content\/uploads\/2023\/03\/A-rectangular-trapezoid-300x173.jpg 300w\" sizes=\"auto, (max-width: 375px) 100vw, 375px\" \/><figcaption class=\"wp-element-caption\">Rectangular<\/figcaption><\/figure>\n<\/div>\n\n\n<p class=\"wp-block-paragraph\">The formula for area takes the following variant:<\/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-rectangular-trapezoid.jpg\" alt=\"Formula for the area of a rectangular\" class=\"wp-image-802\" width=\"250\" height=\"134\" srcset=\"https:\/\/www.matematikazavsicki.com\/en\/wp-content\/uploads\/2023\/03\/Formula-for-the-area-of-a-rectangular-trapezoid.jpg 500w, https:\/\/www.matematikazavsicki.com\/en\/wp-content\/uploads\/2023\/03\/Formula-for-the-area-of-a-rectangular-trapezoid-300x161.jpg 300w\" sizes=\"auto, (max-width: 250px) 100vw, 250px\" \/><\/figure>\n<\/div>\n\n\n<p class=\"wp-block-paragraph\">In the last formula, unlike the general formula for the area of this geometric figure, we can replace the height h with the length of the side c (the side on which they lie, i.e. the two right angles belong).<\/p>\n\n\n\n<p class=\"has-vivid-purple-color has-text-color wp-block-paragraph\">Example number 3: Calculate the area of a trapezoid with bases 15cm and 13cm, if its side c, which forms a right angle with the bases, is 8cm.<\/p>\n\n\n\n<p class=\"has-vivid-purple-color has-text-color wp-block-paragraph\">The calculation for determining the area of a rectangular trapezoid can proceed as follows:<\/p>\n\n\n\n<ol class=\"wp-block-list\">\n<li>The sum a+b is: 15cm + 13cm = 28cm<\/li>\n\n\n\n<li>Then the sum of a+b in division by 2: 28cm : 2 = 14cm<\/li>\n\n\n\n<li>The result of step 2 is in multiplication by the length of side c.<\/li>\n<\/ol>\n\n\n\n<p class=\"wp-block-paragraph\">Finally, the area of the figure from example number three is 112 square centimeters.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">In the end, every trapezoid has two diagonals that are equal in length only in the isosceles. Only the isosceles have one axis of symmetry, while any other (other than the isosceles) has no axis of symmetry.<\/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 class=\"wp-block-paragraph\">Follow the information and materials that will be published in the future. 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The only sufficient condition for a quadrilateral to be a trapezoid is that it has only one pair [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":813,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[3,4,7,12],"tags":[88,68,110,87,111,107,109,108],"class_list":["post-779","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-5th-grade","category-6th-grade","category-9th-grade","category-geometry","tag-area","tag-formula","tag-isosceles-trapezoid","tag-perimeter","tag-rectangular-trapezoid","tag-trapezoid","tag-trapezoids","tag-types"],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v26.5 - https:\/\/yoast.com\/wordpress\/plugins\/seo\/ -->\n<title>Trapezoid and types of trapezoids - Math For All<\/title>\n<meta name=\"description\" content=\"A trapezoid is a quadrilateral that has one pair of parallel sides. 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