{"id":2619,"date":"2021-10-05T08:54:57","date_gmt":"2021-10-05T08:54:57","guid":{"rendered":"http:\/\/stgwebsite.mindspark.in\/wordpress\/?page_id=2619"},"modified":"2022-01-02T13:47:00","modified_gmt":"2022-01-02T13:47:00","slug":"area-of-kite-derivation-formulas-examples","status":"publish","type":"page","link":"https:\/\/stgwebsite.mindspark.in\/studymaterial\/math-concepts\/area-of-kite-derivation-formulas-examples\/","title":{"rendered":"Area of Kite \u2013 Derivation, Formulas, Examples"},"content":{"rendered":"<p>[et_pb_section fb_built=&#8221;1&#8243; admin_label=&#8221;Section&#8221; module_class=&#8221;mainsec&#8221; _builder_version=&#8221;4.10.4&#8243; _module_preset=&#8221;default&#8221; background_color=&#8221;#e0f2fd&#8221; z_index=&#8221;1&#8243; custom_padding=&#8221;5px||5px||true|false&#8221; locked=&#8221;off&#8221; collapsed=&#8221;off&#8221; global_colors_info=&#8221;{}&#8221;][et_pb_row column_structure=&#8221;3_5,2_5&#8243; custom_padding_last_edited=&#8221;on|phone&#8221; _builder_version=&#8221;4.10.8&#8243; _module_preset=&#8221;default&#8221; background_color=&#8221;#FFFFFF&#8221; width=&#8221;100%&#8221; max_width=&#8221;1310px&#8221; custom_padding=&#8221;|51px|40px|51px|false|true&#8221; custom_padding_tablet=&#8221;&#8221; custom_padding_phone=&#8221;|40px|30px|40px|false|true&#8221; border_radii=&#8221;on|10px|10px|10px|10px&#8221; global_colors_info=&#8221;{}&#8221;][et_pb_column type=&#8221;3_5&#8243; admin_label=&#8221;Column L&#8221; _builder_version=&#8221;4.9.10&#8243; _module_preset=&#8221;default&#8221; global_colors_info=&#8221;{}&#8221;][et_pb_text admin_label=&#8221;Acute Angles<br \/>\n&#8221; _builder_version=&#8221;4.11.1&#8243; _module_preset=&#8221;default&#8221; header_font=&#8221;|700|||||||&#8221; header_text_align=&#8221;left&#8221; header_font_size=&#8221;50px&#8221; header_line_height=&#8221;1.18em&#8221; custom_padding=&#8221;|0px||4px|false|false&#8221; header_font_size_tablet=&#8221;&#8221; header_font_size_phone=&#8221;35px&#8221; header_font_size_last_edited=&#8221;on|phone&#8221; global_colors_info=&#8221;{}&#8221;]<\/p>\n<h1><strong>Area of Kite \u2013 Derivation, Formulas, Examples<\/strong><\/h1>\n<p>[\/et_pb_text][et_pb_text admin_label=&#8221;Text&#8221; _builder_version=&#8221;4.11.3&#8243; _module_preset=&#8221;default&#8221; text_font_size=&#8221;16px&#8221; header_2_font=&#8221;|600|||||||&#8221; header_2_text_color=&#8221;#a01414&#8243; header_3_font=&#8221;|600|||||||&#8221; header_3_text_color=&#8221;#898989&#8243; custom_padding=&#8221;15px|15px||4px|false|false&#8221; global_colors_info=&#8221;{}&#8221;]<\/p>\n<h2><strong>What is a kite?<\/strong><\/h2>\n<p>A kite is an irregular quadrilateral with 2 equal pairs of sides adjacent to\u00a0each other.Both the diagonals of the kite intersect each other at right angles.<\/p>\n<p>Here are some properties of a kite<img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/eistudymaterial.s3.amazonaws.com\/Untitfghled.png\" width=\"274\" height=\"342\" alt=\"\" class=\"wp-image-3499 alignnone size-full\" \/><\/p>\n<ul>\n<li>In the figure above, JK = KL and JM = LM, which means that adjacent sides of a kite are equal in length.<\/li>\n<li>Diagonals<span>\u00a0of a kite make an angle of 90 degrees at the point of intersection.<\/span><\/li>\n<li>Angles between unequal sides are equal. Here, \u2220J = \u2220K<\/li>\n<li>The longer diagonal divides the kite into one <strong>pair of congruent triangle.<\/strong><\/li>\n<\/ul>\n<h2><\/h2>\n<h2><strong>What is the area of a kite formed by two perpendicular diagonals?<\/strong><\/h2>\n<p>Half the product of its diagonals gives the <strong>formula for the area of a kite<\/strong>. For example, if the diagonals of a kite are D1 and D2, then:<\/p>\n<p><strong>Area of kite<\/strong> = \u00bd D1 x D2<\/p>\n<p>&nbsp;<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/eistudymaterial.s3.amazonaws.com\/Untitf23ghled.png\" width=\"235\" height=\"133\" alt=\"\" class=\"wp-image-3502 alignnone size-full\" \/><\/p>\n<p>&nbsp;<\/p>\n<p>Let us find the area of the kite PQRS.<\/p>\n<p>Here the diagonals are PR and QS<\/p>\n<p>Let diagonal PR be \u2018a\u2019 and diagonal QS be \u2018b.\u2019<\/p>\n<p>We know the diagonals of a kite bisect each other at right angles.<\/p>\n<p>So, in the figure, diagonal PR bisects diagonal QS.<\/p>\n<p>OQ = OS = OS\/2 =\u00a0 b\/2<\/p>\n<p><strong>Area of the kite<\/strong> = sum of area of triangle PQR and PSR<\/p>\n<p>Area of Triangle =\u00a0\u00bd b\u00d7h<\/p>\n<p>baseis\u2018a\u2019 and height is OQ = OS = OS\/2 =\u00a0 B\/2<\/p>\n<p>Area of triangle PQR =\u00a0\u00bd \u00a0x a x b\/2<\/p>\n<p>Area of triangle PSR=\u00a0\u00bd \u00a0x a x b\/2<\/p>\n<p>So, <strong>area of kite<\/strong> =\u00a0\u00bd \u00a0x a x b\/2+ \u00bd \u00a0x a x b\/2<\/p>\n<p>= ab\/4\u00a0 + ab\/4<\/p>\n<p>= <span> 2ab\/4 = 1\/2ab<\/span><\/p>\n<p>So, the <strong>formula for the area of the kite<\/strong>is \u00bd \u00a0x diagonal1 x diagonal2 = half the product of diagonals<\/p>\n<p>&nbsp;<\/p>\n<h3><strong>An alternate method to find the area of a kite<\/strong><\/h3>\n<p>Consider that you do not know the measure of the kite&#8217;s diagonals; how will you solve the <strong>area of kite questions<\/strong> without the diagonals if you do not know any alternate methods?<\/p>\n<p>Here\u2019s the catch, you can use trigonometry to find the <strong>area of the kite formula with sides<\/strong> and their included angle. You can use the formula,<\/p>\n<p><strong>Area of kite = ab sinC<\/strong><\/p>\n<p>where<\/p>\n<p>a and b denote the measure of unequal sides<\/p>\n<p>c is the internal angle between them<\/p>\n<p>and sin is the sine function in trigonometry<\/p>\n<p>&nbsp;<\/p>\n<h3><strong>Examples<\/strong><\/h3>\n<p><strong>Example 1<\/strong><\/p>\n<p>How can you prove the area of the kite is equal to the area of the rhombus?<\/p>\n<p><strong>Solution<\/strong><\/p>\n<p>We explain to you how tocalculate the area of a rhombus by drawing two diagonals d1 and d2. These two diagonals are perpendicular to each other and bisect each other. So, one diagonal splits the rhombus into two equal triangles. Hence, the area of a rhombus is equal to the sum of the area of these two triangles.<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/eistudymaterial.s3.amazonaws.com\/Untitf23ghled.png\" width=\"226\" height=\"180\" alt=\"\" class=\"wp-image-3503 alignnone size-full\" \/><\/p>\n<p>&nbsp;<\/p>\n<p>So, area of triangle ADC = area of triangle ABC = \u00bd \u00a0x d1 x d2\/2<\/p>\n<p>Area of rhombus = area of ADC + area of triangle ABC<\/p>\n<p>Area of rhombus = \u00bd x d1 x d2\/2 + \u00bd \u00a0x d1 x d2\/2<\/p>\n<p>= \u00bd x d1 x d2<\/p>\n<p>Considering this, the <strong>area of the kite and rhombus<\/strong> is the same.<\/p>\n<p>&nbsp;<\/p>\n<p><strong>Example 2<\/strong><\/p>\n<p>Calculate the area of a kite with diagonals 24cm and 10cm<\/p>\n<p><strong>Solution<\/strong><\/p>\n<p>Area of kite =\u00a0 \u00bd x d1 x d2<\/p>\n<p>=\u00bd \u00a0x 24 x 10 cm<sup>2<\/sup><\/p>\n<p>= 120 cm<sup>2<\/sup><\/p>\n<p>Therefore, the area of kite = 120 cm<sup>2<\/sup><\/p>\n<p>[\/et_pb_text][et_pb_text disabled_on=&#8221;on|on|on&#8221; admin_label=&#8221;Sample Questions<br \/>\n&#8221; _builder_version=&#8221;4.10.8&#8243; _module_preset=&#8221;default&#8221; header_font=&#8221;|700|||||||&#8221; header_font_size=&#8221;28px&#8221; custom_padding=&#8221;|0px||4px|false|false&#8221; disabled=&#8221;on&#8221; global_colors_info=&#8221;{}&#8221;]<\/p>\n<h1>Practice Multiple Choice Questions<\/h1>\n<p>[\/et_pb_text][et_pb_text disabled_on=&#8221;on|on|on&#8221; admin_label=&#8221;Question 1&#8243; _builder_version=&#8221;4.11.1&#8243; _module_preset=&#8221;default&#8221; background_color=&#8221;#FFFFFF&#8221; custom_padding=&#8221;25px|25px|25px|25px|true|true&#8221; border_radii=&#8221;on|15px|15px|15px|15px&#8221; border_width_all=&#8221;2px&#8221; border_color_all=&#8221;#000000&#8243; border_width_top=&#8221;4px&#8221; border_color_top=&#8221;#E02B20&#8243; disabled=&#8221;on&#8221; global_colors_info=&#8221;{}&#8221;]<\/p>\n<div class=\"qmanage\">\n<div class=\"qq\">\n<p><strong>Questions<\/strong><\/p>\n<p><b>Example 1<\/b><\/p>\n<p><span style=\"font-weight: 400;\">How can you prove the area of the kite is equal to the area of the rhombus?<\/span><\/p>\n<p><b>Solution<\/b><\/p>\n<p><span style=\"font-weight: 400;\">We explain to you how to calculate the area of a rhombus by drawing two diagonals d1 and d2. These two diagonals are perpendicular to each other and bisect each other. So, one diagonal splits the rhombus into two equal triangles. Hence, the area of a rhombus is equal to the sum of the area of these two triangles.<\/span><\/p>\n<p><span style=\"font-weight: 400;\">So, area of triangle ADC = area of triangle ABC = <\/span><span style=\"font-weight: 400;\">1<\/span><span style=\"font-weight: 400;\">2<\/span><span style=\"font-weight: 400;\"> x d1 x <\/span><span style=\"font-weight: 400;\">d2<\/span><span style=\"font-weight: 400;\">2<\/span><\/p>\n<p><span style=\"font-weight: 400;\">Area of rhombus = area of ADC + area of triangle ABC<\/span><\/p>\n<p><span style=\"font-weight: 400;\">Area of rhombus = <\/span><span style=\"font-weight: 400;\">1<\/span><span style=\"font-weight: 400;\">2<\/span><span style=\"font-weight: 400;\"> x d1 x <\/span><span style=\"font-weight: 400;\">d2<\/span><span style=\"font-weight: 400;\">2<\/span><span style=\"font-weight: 400;\"> + <\/span><span style=\"font-weight: 400;\">1<\/span><span style=\"font-weight: 400;\">2<\/span><span style=\"font-weight: 400;\"> x d1 x <\/span><span style=\"font-weight: 400;\">d2<\/span><span style=\"font-weight: 400;\">2<\/span><\/p>\n<p><span style=\"font-weight: 400;\">= <\/span><span style=\"font-weight: 400;\">1<\/span><span style=\"font-weight: 400;\">2<\/span><span style=\"font-weight: 400;\"> x d1 x d2<\/span><\/p>\n<p><span style=\"font-weight: 400;\">Considering this, the <\/span><b>area of the kite and rhombus<\/b><span style=\"font-weight: 400;\"> is the same.<\/span><\/p>\n<p>&nbsp;<\/p>\n<p><b>Example 2<\/b><\/p>\n<p><span style=\"font-weight: 400;\">Calculate the area of a kite with diagonals 24cm and 10cm<\/span><\/p>\n<p><b>Solution<\/b><\/p>\n<p><span style=\"font-weight: 400;\">Area of kite =\u00a0 <\/span><span style=\"font-weight: 400;\">1<\/span><span style=\"font-weight: 400;\">2<\/span><span style=\"font-weight: 400;\"> x d1 x d2<\/span><\/p>\n<p><span style=\"font-weight: 400;\">= <\/span><span style=\"font-weight: 400;\">1<\/span><span style=\"font-weight: 400;\">2<\/span><span style=\"font-weight: 400;\"> x 24 x 10 cm<\/span><span style=\"font-weight: 400;\">2<\/span><\/p>\n<p><span style=\"font-weight: 400;\">= 120 cm<\/span><span style=\"font-weight: 400;\">2<\/span><\/p>\n<p><span style=\"font-weight: 400;\">Therefore, <\/span><span style=\"font-weight: 400;\">the area of kite = 120 cm<\/span><span style=\"font-weight: 400;\">2<\/span><\/p>\n<\/div>\n<\/div>\n<p>[\/et_pb_text][\/et_pb_column][et_pb_column type=&#8221;2_5&#8243; 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_module_preset=&#8221;default&#8221; width=&#8221;100%&#8221; max_width=&#8221;1310px&#8221; custom_padding=&#8221;|40px||40px|false|true&#8221; global_colors_info=&#8221;{}&#8221;][et_pb_column type=&#8221;4_4&#8243; _builder_version=&#8221;4.9.11&#8243; _module_preset=&#8221;default&#8221; global_colors_info=&#8221;{}&#8221;][et_pb_text admin_label=&#8221;FAQ&#8221; module_class=&#8221;faqstyl&#8221; _builder_version=&#8221;4.11.3&#8243; _module_preset=&#8221;default&#8221; text_font_size=&#8221;16px&#8221; header_font=&#8221;|700|||||||&#8221; header_text_align=&#8221;center&#8221; header_line_height=&#8221;2.5em&#8221; background_color=&#8221;#dbedc6&#8243; max_width=&#8221;80%&#8221; module_alignment=&#8221;center&#8221; custom_margin=&#8221;||||false|false&#8221; custom_padding=&#8221;30px|25px|30px|25px|true|true&#8221; border_radii=&#8221;on|10px|10px|10px|10px&#8221; global_colors_info=&#8221;{}&#8221;]<\/p>\n<h1>Frequently Asked Questions<span style=\"font-weight: 400;\"><span style=\"font-weight: 400;\">\u00a0<\/span><\/span><\/h1>\n<p><span style=\"font-weight: 400;\"><strong>1.<\/strong> State one difference between a kite and a rhombus.<\/span><br \/><span style=\"font-weight: 400;\"><strong>Ans<\/strong>: A rhombus is a quadrilateral with four congruent sides, whereas in a kite each pair of adjacent sides is congruent.<\/span><\/p>\n<p><span style=\"font-weight: 400;\"><strong>2<\/strong>. How to calculate the measure of diagonals of a kite?<\/span><br \/><span style=\"font-weight: 400;\"><strong>Ans<\/strong>: You can calculate the length of the diagonal of a kite by using Pythagoras Theorem, then substituting the value of diagonal1 in the <\/span><b>area of the kite formula<\/b><span style=\"font-weight: 400;\"> to find the measure of diagonal2.\u00a0<\/span><br \/><span style=\"font-weight: 400;\">Note that this step is only applicable if you know the area of the kite.<\/span><\/p>\n<p><span style=\"font-weight: 400;\"><strong>3<\/strong>. State the <\/span><b>formula for the area of the kite<\/b><span style=\"font-weight: 400;\">.<\/span><br \/><span style=\"font-weight: 400;\"><strong>Ans<\/strong>: The formula for the area of a kite is<\/span> <span style=\"font-weight: 400;\">1\/<\/span><span style=\"font-weight: 400;\">2<\/span><span style=\"font-weight: 400;\"> x d1 x d2<\/span><\/p>\n<p>[\/et_pb_text][\/et_pb_column][\/et_pb_row][\/et_pb_section]<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Numbers can be expressed in words and we call them number names. The numbers starting from 1 to 20 are written with specific spellings followed by a generic pattern. <\/p>\n","protected":false},"author":7,"featured_media":0,"parent":714,"menu_order":0,"comment_status":"closed","ping_status":"closed","template":"","meta":{"_et_pb_use_builder":"on","_et_pb_old_content":"","_et_gb_content_width":"","footnotes":""},"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v17.6 - https:\/\/yoast.com\/wordpress\/plugins\/seo\/ -->\n<title>Area of Kite \u2013 Derivation, Formulas, Examples - mydomain<\/title>\n<meta name=\"description\" content=\"The area of a kite is 12 d1 d2, where d1 and d2 are the diagonals of the kite. You can also find the area of the kite through trigonometry if the diagonals are not given.\" \/>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/stgwebsite.mindspark.in\/studymaterial\/math-concepts\/area-of-kite-derivation-formulas-examples\/\" \/>\n<meta property=\"og:locale\" content=\"en_US\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"Area of Kite \u2013 Derivation, Formulas, Examples - mydomain\" \/>\n<meta property=\"og:description\" content=\"The area of a kite is 12 d1 d2, where d1 and d2 are the diagonals of the kite. 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