A hexagon is a six-sided polygon. We call a hexagon a regular hexagon when all the six sides and angles are equal. The measure of every angle in a regular hexagon is 120\u00b0.<\/span><\/p>\n <\/span><\/p>\n <\/span><\/p>\n Area of regular hexagon means the measure of the surface covered by the hexagon. The formula for the area of a regular hexagon is\\frac{3 \\sqrt{3} a^{2}}{2}<\/span>where \u2018a\u2019 is the side of the regular hexagon.<\/span><\/strong><\/p>\n <\/span><\/strong><\/p>\n DERIVATION:<\/strong><\/p>\n Take a regular hexagon with side \u2018a\u2019. Join all the vertices\u00a0 which are opposite to each other like shown in the figure below:<\/span><\/p>\n <\/span><\/p>\n <\/span><\/p>\n Now, when we join the vertices opposite to each other, 6 triangles are formed of equal sides and angles.<\/span><\/p>\n As we can see in \u0394 AOB, each angle is 60\u00b0.<\/span><\/p>\n Therefore we know when in a triangle all the angles are equal, it is known as an equilateral triangle.<\/span><\/p>\n We know that Formula of Area of\u00a0 Equilateral Triangle =\\frac{\\sqrt{3} a^{2}}{4}<\/span>where \u2018a\u2019 is the side of the equilateral triangle.<\/span><\/p>\n Area of regular hexagon<\/span><\/p>\n = Area of\u00a0 \u0394 AOB +\u00a0 Area of\u00a0 \u0394 BOC + Area of\u00a0 \u0394 COD + Area of\u00a0 \u0394 DOE + Area of\u00a0 \u0394 EOF + Area of\u00a0 \u0394 FOA<\/span><\/p>\n = \\frac{\\sqrt{3} a^{2}}{4}+\\frac{\\sqrt{3} a^{2}}{4}+\\frac{\\sqrt{3} a^{2}}{4}+\\frac{\\sqrt{3} a^{2}}{4}+\\frac{\\sqrt{3} a^{2}}{4}+\\frac{\\sqrt{3} a^{2}}{4}<\/span><\/span><\/p>\n = 6 \\times \\frac{\\sqrt{3} a^{2}}{4}<\/span><\/span><\/p>\n Area of regular hexagon =\\frac{3 \\sqrt{3} a^{2}}{2}<\/span>, where a is the side of the regular hexagon.<\/span><\/p>\n <\/p>\n 1. Find the area of a hexagon whose each side measures 8 \\sqrt{2} \\mathrm{~cm}<\/span>?<\/span><\/p>\n Solution:<\/span><\/p>\n Area of regular hexagon=\\frac{3 \\sqrt{3} a^{2}}{2}<\/span><\/span><\/p>\n where ‘a’ is the side of the regular hexagon.<\/span><\/p>\n Area of the given regular hexagon =\\frac{3 \\sqrt{3} \\times(8 \\times \\sqrt{2})^{2}}{2}=\\frac{3 \\sqrt{3} \\times 64 \\times 2}{2}=192 \\sqrt{3} \\mathrm{~cm}^{2}<\/span><\/span><\/p>\n <\/span><\/p>\n 2. Find the side of the regular hexagon whose area is 150 \\sqrt{3} \\mathrm{~cm}^{2}<\/span><\/span><\/p>\n Solution:<\/span><\/p>\n Area of regular hexagon =\\frac{3 \\sqrt{3} a^{2}}{2}<\/span><\/span><\/p>\n \u2234 150 \\sqrt{3}=\\frac{3 \\sqrt{3} a^{2}}{2}<\/span><\/span><\/p>\n \u21d2 50 \\times 2=a^{2} <\/span> Therefore the length of the side of a regular hexagon will be 10 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” hover_enabled=”0″ locked=”off” global_colors_info=”{}” sticky_enabled=”0″]<\/p>\n![\"\"](\"https:\/\/eistudymaterial.s3.amazonaws.com\/AREA-OF-REGULAR-HEXAGON-01-300x104.png\")
<\/span><\/p>\nArea Of Regular Hexagon<\/strong><\/h2>\n
![\"\"](\"https:\/\/eistudymaterial.s3.amazonaws.com\/AREA-OF-REGULAR-HEXAGON-02-252x300.png\")
<\/span><\/p>\nExamples<\/strong><\/h2>\n
\u21d2 100=a^{2} <\/span>
\u21d2 a=10<\/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