<\/span><\/p>\n In \u25b3ABC,<\/span><\/p>\n Hence it is an isosceles right triangle<\/span><\/p>\n <\/p>\n Area =\\frac{1}{2} a^{2}<\/span><\/span><\/b><\/p>\n Where a = length of a leg<\/span><\/p>\n <\/span><\/p>\n We already know that the area of a triangle is given by the following formula<\/span><\/p>\n \\text { Area }=\\frac{1}{2} \\times \\text { base } \\times \\text { height }<\/span><\/span><\/p>\n In \u25b3ABC, <\/span>\u2220ABC = 90\u00b0<\/span><\/p>\n Hence BC is the base and AB is the height of the triangle.<\/span><\/p>\n Base = BC = a\u00a0<\/span><\/p>\n Height = AB = a\u00a0<\/span><\/p>\n \\text { Area of } \\triangle \\mathrm{ABC}<\/span><\/span><\/p>\n <\/span><\/p>\n =\\frac{1}{2} \\times \\text { base } \\times \\text { height } <\/span><\/span><\/p>\n <\/p>\n =\\frac{1}{2} \\times a^{2}<\/span><\/span><\/p>\n Hence it is proved that the area of an isosceles right triangle is\u00a0 \\frac{1}{2} a^{2}<\/span>, <\/span>where a is the length of the leg of the triangle.<\/span><\/p>\n <\/span><\/p>\n <\/b><\/p>\n 1. In a right-angled triangle, two sides are equal, having a length of 7 cm. Find the area of this triangle?<\/b><\/p>\n Solution:<\/strong><\/p>\n Since two sides of the right-angled triangle are equal, it is an isosceles right triangle.<\/span><\/p>\n Length of the leg = a = 7 cm<\/span><\/p>\n \\text { Area of the right- angled triangle }<\/span><\/span><\/p>\n <\/span><\/p>\n =\\frac{1}{2} \\times a^{2} <\/span><\/span><\/p>\n \u00a0The area of this triangle is 24.5 \\mathrm{~cm}^{2}<\/span> <\/span><\/p>\n 2. The area of a triangle is 18 cm<\/b>\u00b2<\/b>. What is the length of the hypotenuse if it is an isosceles right triangle?<\/b><\/p>\n Solution:<\/strong><\/p>\n We know that\u00a0<\/span><\/p>\n \\text { Area }=\\frac{1}{2} \\times a^{2}<\/span><\/span><\/p>\n Where a = length of the leg<\/span><\/p>\n It is given that<\/span><\/p>\n \\text { Area }=18 \\mathrm{~cm}^{2}<\/span><\/span><\/p>\n \\Rightarrow \\frac{1}{2} \\times a^{2}=18 <\/span><\/span><\/p>\n Since two sides are equal in an isosceles right triangle, according to Pythagoras theorem we can write that<\/span><\/p>\n {\\text{Side}} ^{2}+{\\text{Side}} ^{2}={\\text{hypotenuse}} ^{2}<\/span><\/span><\/p>\n Hence the length of the hypotenuse is 6<\/span>\u221a2<\/span> cm.<\/span><\/p>\n [\/et_pb_text][\/et_pb_column][et_pb_column type=”2_5″ module_id=”stickysideR” admin_label=”Column R” _builder_version=”4.10.4″ _module_preset=”default” background_color=”#fdefe0″ custom_padding=”25px|25px|25px|25px|true|true” sticky_position=”top” sticky_offset_top=”-280px” sticky_limit_top=”row” sticky_limit_bottom=”row” sticky_position_tablet=”none” sticky_position_phone=”none” sticky_position_last_edited=”on|desktop” sticky_limit_bottom_tablet=”” sticky_limit_bottom_phone=”” sticky_limit_bottom_last_edited=”on|phone” border_radii=”on|15px|15px|15px|15px” box_shadow_style=”preset3″ global_colors_info=”{}”][et_pb_image src=”https:\/\/eistudymaterial.s3.amazonaws.com\/1080×1080.png” alt=”Free Trial banner” title_text=”Mindspark Free Trial Banner” url=”https:\/\/mindspark.in\/free-trial” align=”center” module_class=”adsimg” _builder_version=”4.11.1″ _module_preset=”default” custom_padding=”||||false|false” border_radii=”on|10px|10px|10px|10px” global_colors_info=”{}” transform_styles__hover_enabled=”on|hover” transform_scale__hover_enabled=”on|hover” transform_translate__hover_enabled=”on|desktop” transform_rotate__hover_enabled=”on|desktop” transform_skew__hover_enabled=”on|desktop” transform_origin__hover_enabled=”on|desktop” transform_scale__hover=”102%|102%”][\/et_pb_image][et_pb_text admin_label=”Explore Other Topics [\/et_pb_text][et_pb_text _builder_version=”4.10.7″ _module_preset=”default” text_line_height=”2.2em” link_font_size=”16px” custom_margin=”||0px||false|false” custom_padding=”10px|15px|10px|28px|true|false” locked=”off” global_colors_info=”{}”]<\/p>\n [\/et_pb_text][et_pb_text admin_label=”Related Concepts [\/et_pb_text][et_pb_text _builder_version=”4.13.1″ _module_preset=”default” text_line_height=”2.2em” link_font_size=”16px” custom_margin=”||0px||false|false” custom_padding=”10px|15px|10px|28px|true|false” locked=”off” global_colors_info=”{}”]<\/p>\n [\/et_pb_text][\/et_pb_column][\/et_pb_row][et_pb_row admin_label=”Row for space” _builder_version=”4.10.6″ _module_preset=”default” locked=”off” global_colors_info=”{}”][et_pb_column type=”4_4″ _builder_version=”4.9.11″ _module_preset=”default” global_colors_info=”{}”][et_pb_divider show_divider=”off” _builder_version=”4.10.4″ _module_preset=”default” global_colors_info=”{}”][\/et_pb_divider][\/et_pb_column][\/et_pb_row][\/et_pb_section][et_pb_section fb_built=”1″ admin_label=”banner and faq Section” module_class=”mainsec2″ _builder_version=”4.10.4″ _module_preset=”default” custom_padding=”40px||0px||false|false” global_colors_info=”{}”][et_pb_row use_custom_gutter=”on” gutter_width=”1″ make_equal=”on” disabled_on=”on|on|off” admin_label=”banner Row” _builder_version=”4.10.4″ _module_preset=”default” background_color=”#fff7d6″ width=”100%” max_width=”1310px” height=”134px” custom_margin=”||50px||false|false” custom_padding=”12px||12px||true|false” border_radii=”on|11px|11px|11px|11px” locked=”off” collapsed=”off” global_colors_info=”{}”][et_pb_column type=”4_4″ _builder_version=”4.9.10″ _module_preset=”default” global_colors_info=”{}”][et_pb_image src=”https:\/\/stgwebsite.mindspark.in\/wordpress\/wp-content\/uploads\/2021\/08\/calloutImage.png” title_text=”calloutImage” show_bottom_space=”off” admin_label=”Image” module_class=”img1″ _builder_version=”4.10.8″ _module_preset=”default” width=”25px” height=”60px” custom_padding=”2px||2px||true|false” global_colors_info=”{}”][\/et_pb_image][et_pb_text module_class=”ftstyle” _builder_version=”4.9.10″ _module_preset=”default” text_orientation=”center” global_colors_info=”{}”]<\/p>\n![\"\"](\"https:\/\/eistudymaterial.s3.amazonaws.com\/Area-of-isosceles-right-triangle-01.png\")
<\/span><\/p>\n\n
The formula for finding the area<\/b><\/h2>\n
Derivation of the formula<\/b><\/h2>\n
<\/b><\/p>\n
=\\frac{1}{2} \\times \\mathrm{BC} \\times \\mathrm{AB} <\/span><\/span><\/p>\n
=\\frac{1}{2} \\times \\mathrm{a} \\times \\mathrm{a}<\/span><\/span><\/p>\nSolved Examples.<\/b><\/h2>\n
=\\left(\\frac{1}{2} \\times 7^{2}\\right) \\mathrm{cm}^{2} <\/span><\/span><\/p>\n
=\\left(\\frac{1}{2} \\times 49\\right) \\mathrm{cm}^{2} <\/span><\/span><\/p>\n
=24.5 \\mathrm{~cm}^{2}<\/span><\/span><\/p>\n
<\/span><\/p>\n
\\Rightarrow a^{2}=18 \\times 2=36 <\/span><\/span><\/p>\n
\\Rightarrow a=\\sqrt{36}=6 \\mathrm{~cm}<\/span><\/span><\/p>\n
{\\text{Hypotenuse}} ^{2}=a^{2}+a^{2}=2 a^{2}=2 \\times 6^{2}=2 \\times 36=72<\/span><\/span><\/p>\n
{\\text{Hypotenuse}} =\\sqrt{72}=6 \\sqrt{2} \\mathrm{~cm}<\/span><\/span><\/p>\n
\n” _builder_version=”4.9.11″ _module_preset=”default” header_font=”|700|||||||” header_font_size=”25px” text_orientation=”center” custom_margin=”0px||0px||true|false” custom_padding=”8px|15px|0px|15px|false|true” locked=”off” global_colors_info=”{}”]<\/p>\nExplore Other Topics<\/h1>\n
\n” _builder_version=”4.9.11″ _module_preset=”default” header_font=”|700|||||||” header_font_size=”25px” text_orientation=”center” custom_margin=”0px||0px||true|false” custom_padding=”8px|15px|0px|15px|false|true” locked=”off” global_colors_info=”{}”]<\/p>\nRelated Concepts<\/h1>\n