{"id":4957,"date":"2021-12-01T15:25:54","date_gmt":"2021-12-01T15:25:54","guid":{"rendered":"https:\/\/stgwebsite.mindspark.in\/studymaterial\/?page_id=4957"},"modified":"2021-12-03T08:12:13","modified_gmt":"2021-12-03T08:12:13","slug":"convex-polygon-with-examples-and-faqs","status":"publish","type":"page","link":"https:\/\/stgwebsite.mindspark.in\/studymaterial\/math-concepts\/convex-polygon-with-examples-and-faqs\/","title":{"rendered":"Convex Polygon with Examples and FAQs"},"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;4.11.3&#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>Convex Polygon with Examples and FAQs<\/h1>\n<p>[\/et_pb_text][et_pb_text admin_label=&#8221;Text&#8221; _builder_version=&#8221;4.13.1&#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; custom_padding=&#8221;15px|15px|54px|4px|false|false&#8221; hover_enabled=&#8221;0&#8243; global_colors_info=&#8221;{}&#8221; sticky_enabled=&#8221;0&#8243;]<\/p>\n<h2><b>Convex Polygon Definition<\/b><\/h2>\n<p><span style=\"font-weight: 400;\">A Polygon is a closed two-dimensional figure which has more than two sides, vertices and interior angles. The polygons which have all the vertices pointing outwards and each of its interior angles measuring less than 180<\/span><span style=\"font-weight: 400;\">\u00b0<\/span><span style=\"font-weight: 400;\"> are convex polygons.<\/span><\/p>\n<p><span style=\"font-weight: 400;\">The images below are some examples of such polygons:<\/span><\/p>\n<p><span style=\"font-weight: 400;\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/eistudymaterial.s3.amazonaws.com\/triangle1.png\" width=\"200\" height=\"178\" alt=\"\" class=\"wp-image-4963 alignnone size-full\" \/> <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/eistudymaterial.s3.amazonaws.com\/triangle2.png\" width=\"189\" height=\"185\" alt=\"\" class=\"wp-image-4962 alignnone size-full\" \/> <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/eistudymaterial.s3.amazonaws.com\/hexagon-300x263.png\" width=\"232\" height=\"203\" alt=\"\" class=\"wp-image-5135 alignnone size-medium\" srcset=\"https:\/\/eistudymaterial.s3.amazonaws.com\/hexagon-300x263.png 300w, https:\/\/eistudymaterial.s3.amazonaws.com\/hexagon.png 409w\" sizes=\"(max-width: 232px) 100vw, 232px\" \/><\/span><\/p>\n<h4><b><\/b><\/h4>\n<h4><b>Note:<\/b><\/h4>\n<h4><strong>Concave Polygon<\/strong><\/h4>\n<p><span style=\"font-weight: 400;\">The polygons which have vertices which are a combination of both inwards and outwards and at least one angle measuring greater than 180\u00b0 are concave polygons.<\/span><\/p>\n<p><span style=\"font-weight: 400;\">The images below are some examples of concave polygons.<\/span><\/p>\n<p style=\"text-align: center;\"><span style=\"font-weight: 400;\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/eistudymaterial.s3.amazonaws.com\/2pics-300x137.png\" width=\"501\" height=\"229\" alt=\"\" class=\"wp-image-4960 alignnone size-medium\" srcset=\"https:\/\/eistudymaterial.s3.amazonaws.com\/2pics-300x137.png 300w, https:\/\/eistudymaterial.s3.amazonaws.com\/2pics-1024x469.png 1024w, https:\/\/eistudymaterial.s3.amazonaws.com\/2pics-768x352.png 768w, https:\/\/eistudymaterial.s3.amazonaws.com\/2pics-1080x495.png 1080w, https:\/\/eistudymaterial.s3.amazonaws.com\/2pics-1280x586.png 1280w, https:\/\/eistudymaterial.s3.amazonaws.com\/2pics-980x449.png 980w, https:\/\/eistudymaterial.s3.amazonaws.com\/2pics-480x220.png 480w, https:\/\/eistudymaterial.s3.amazonaws.com\/2pics.png 1284w\" sizes=\"(max-width: 501px) 100vw, 501px\" \/><\/span><\/p>\n<h2><b>Properties<\/b><b><\/b><\/h2>\n<p><span style=\"font-weight: 400;\">The properties of convex polygons are:<\/span><span style=\"font-weight: 400;\"><\/span><\/p>\n<ul>\n<li style=\"font-weight: 400;\" aria-level=\"1\"><span style=\"font-weight: 400;\">All interior angles measure less than 180<\/span><span style=\"font-weight: 400;\">\u00b0<\/span><span style=\"font-weight: 400;\">.<\/span><\/li>\n<li style=\"font-weight: 400;\" aria-level=\"1\"><span style=\"font-weight: 400;\">All diagonals lie inside the polygon itself.<\/span><\/li>\n<li style=\"font-weight: 400;\" aria-level=\"1\"><span style=\"font-weight: 400;\">The line joining any two points on the polygon lies completely inside the polygon.\u00a0<\/span><\/li>\n<\/ul>\n<p><span style=\"font-weight: 400;\"><\/span><\/p>\n<p><span style=\"font-weight: 400;\"><\/span><\/p>\n<h2><b>Sum of Angles of a Convex Polygon:<\/b><\/h2>\n<h3><b><\/b><\/h3>\n<h3><b>Interior angles<\/b><\/h3>\n<p><span style=\"font-weight: 400;\">The sum of the interior angles of a convex polygon with \u2018<\/span><b>n<\/b><span style=\"font-weight: 400;\">\u2019 number of sides can be found out by the formula:<\/span><\/p>\n<p><span style=\"font-weight: 400;\"><span class=\"katex-eq\" data-katex-display=\"false\">[180\\times (n-2)]^\\circ<\/span><\/span><\/p>\n<p><span style=\"font-weight: 400;\">If the polygon is regular it will have all sides and interior angles of equal measure.<\/span><\/p>\n<p><span style=\"font-weight: 400;\">For example, we know for a triangle sum of interior angles is 180<\/span><span style=\"font-weight: 400;\">\u00b0<\/span><span style=\"font-weight: 400;\">, let us verify this using the formula above<\/span><b>:<\/b><\/p>\n<p><span style=\"font-weight: 400;\">For a triangle the value of n = 3,<\/span><\/p>\n<p><span style=\"font-weight: 400;\">Sum of interior angles <span class=\"katex-eq\" data-katex-display=\"false\">=[180 \\times(n-2)]^{\\circ}=[180 \\times(3-2)]^{\\circ}=[180 \\times 1]^{\\circ}=180^{\\circ} .<\/span><\/span><\/p>\n<p><span style=\"font-weight: 400;\"><\/span><\/p>\n<h3><b>Exterior angles<\/b><\/h3>\n<p><span style=\"font-weight: 400;\">The sum of all exterior angles of a convex polygon is 360<\/span><span style=\"font-weight: 400;\">\u00b0<\/span><span style=\"font-weight: 400;\">, irrespective of the number of sides of the polygon.<\/span><\/p>\n<p><span style=\"font-weight: 400;\">For a regular polygon i.e., when the measure of all sides is equivalent, each exterior angle is equal to <span class=\"katex-eq\" data-katex-display=\"false\">\\frac{360^{\\circ}}{n}<\/span><\/span><span style=\"font-weight: 400;\">, where \u2018n\u2019 is the number of sides.<\/span><\/p>\n<p><span style=\"font-weight: 400;\"><\/span><\/p>\n<h2><b>Number of diagonals<\/b><\/h2>\n<p><span style=\"font-weight: 400;\">The number of diagonals for a polygon having \u2018n\u2019 sides is given by the formula:<\/span><\/p>\n<p><span style=\"font-weight: 400;\"><span class=\"katex-eq\" data-katex-display=\"false\">\\frac{n(n-3)}{2}<\/span><\/span><\/p>\n<p><span style=\"font-weight: 400;\"><\/span><\/p>\n<h2><b>Examples<\/b><\/h2>\n<p><b><\/b><\/p>\n<p><strong>Example 1<\/strong><span style=\"font-weight: 400;\"><strong>:<\/strong> Can you determine which polygons are convex in nature from the options given.<\/span><\/p>\n<p style=\"text-align: center;\"><span style=\"font-weight: 400;\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/eistudymaterial.s3.amazonaws.com\/4pics-300x137.png\" width=\"501\" height=\"229\" alt=\"\" class=\"wp-image-4959 alignnone size-medium\" srcset=\"https:\/\/eistudymaterial.s3.amazonaws.com\/4pics-300x137.png 300w, https:\/\/eistudymaterial.s3.amazonaws.com\/4pics-1024x469.png 1024w, https:\/\/eistudymaterial.s3.amazonaws.com\/4pics-768x352.png 768w, https:\/\/eistudymaterial.s3.amazonaws.com\/4pics-1080x495.png 1080w, https:\/\/eistudymaterial.s3.amazonaws.com\/4pics-1280x586.png 1280w, https:\/\/eistudymaterial.s3.amazonaws.com\/4pics-980x449.png 980w, https:\/\/eistudymaterial.s3.amazonaws.com\/4pics-480x220.png 480w, https:\/\/eistudymaterial.s3.amazonaws.com\/4pics.png 1284w\" sizes=\"(max-width: 501px) 100vw, 501px\" \/><\/span><\/p>\n<p><span style=\"font-weight: 400;\"><\/span><\/p>\n<p><strong>Solution<\/strong><span style=\"font-weight: 400;\"><strong>:<\/strong> (A) and (C) are convex polygons, whereas (B) and (D) are concave polygons.<\/span><\/p>\n<p><span style=\"font-weight: 400;\"><\/span><\/p>\n<p><strong>Example 2<\/strong><span style=\"font-weight: 400;\"><strong>:<\/strong> If a polygon that is convex has 10 sides, then what is the sum of its interior angles?\u00a0<\/span><\/p>\n<p><strong>Solution:<\/strong><\/p>\n<p><span style=\"font-weight: 400;\">The sum of interior angles of a convex polygon with \u2018<\/span><b>n<\/b><span style=\"font-weight: 400;\">\u2019 sides is given by the formula:<\/span><\/p>\n<p><span style=\"font-weight: 400;\"><span class=\"katex-eq\" data-katex-display=\"false\">[180\\times (n-2)]^\\circ<\/span><\/span><span style=\"font-weight: 400;\">.<\/span><\/p>\n<p><span style=\"font-weight: 400;\">The given polygon has 10 sides. Hence, the total sum of all its angles<\/span><\/p>\n<p><span style=\"font-weight: 400;\">= [180 \u00d7 (<\/span><span style=\"font-weight: 400;\">10 &#8211; 2)<\/span><span style=\"font-weight: 400;\">]\u00b0<\/span><\/p>\n<p><span style=\"font-weight: 400;\">= [180 \u00d7 8]\u00b0<\/span><\/p>\n<p><span style=\"font-weight: 400;\">= 1440\u00b0<\/span><\/p>\n<p><span style=\"font-weight: 400;\">Hence, the sum of all the interior angles of the polygon is <\/span><span style=\"font-weight: 400;\">1440\u00b0<\/span><span style=\"font-weight: 400;\">.<\/span><\/p>\n<p>[\/et_pb_text][\/et_pb_column][et_pb_column type=&#8221;2_5&#8243; module_id=&#8221;stickysideR&#8221; admin_label=&#8221;Column R&#8221; _builder_version=&#8221;4.10.4&#8243; _module_preset=&#8221;default&#8221; background_color=&#8221;#fdefe0&#8243; custom_padding=&#8221;25px|25px|25px|25px|true|true&#8221; sticky_position=&#8221;top&#8221; sticky_offset_top=&#8221;-280px&#8221; sticky_limit_top=&#8221;row&#8221; sticky_limit_bottom=&#8221;row&#8221; sticky_position_tablet=&#8221;none&#8221; sticky_position_phone=&#8221;none&#8221; sticky_position_last_edited=&#8221;on|desktop&#8221; sticky_limit_bottom_tablet=&#8221;&#8221; sticky_limit_bottom_phone=&#8221;&#8221; sticky_limit_bottom_last_edited=&#8221;on|phone&#8221; border_radii=&#8221;on|15px|15px|15px|15px&#8221; box_shadow_style=&#8221;preset3&#8243; global_colors_info=&#8221;{}&#8221;][et_pb_image src=&#8221;https:\/\/eistudymaterial.s3.amazonaws.com\/1080&#215;1080.png&#8221; alt=&#8221;Free Trial banner&#8221; title_text=&#8221;Mindspark Free Trial Banner&#8221; url=&#8221;https:\/\/mindspark.in\/free-trial&#8221; align=&#8221;center&#8221; module_class=&#8221;adsimg&#8221; _builder_version=&#8221;4.11.1&#8243; _module_preset=&#8221;default&#8221; custom_padding=&#8221;||||false|false&#8221; border_radii=&#8221;on|10px|10px|10px|10px&#8221; global_colors_info=&#8221;{}&#8221; transform_styles__hover_enabled=&#8221;on|hover&#8221; transform_scale__hover_enabled=&#8221;on|hover&#8221; transform_translate__hover_enabled=&#8221;on|desktop&#8221; transform_rotate__hover_enabled=&#8221;on|desktop&#8221; transform_skew__hover_enabled=&#8221;on|desktop&#8221; transform_origin__hover_enabled=&#8221;on|desktop&#8221; transform_scale__hover=&#8221;102%|102%&#8221;][\/et_pb_image][et_pb_text admin_label=&#8221;Explore Other Topics<br \/>\n&#8221; _builder_version=&#8221;4.9.11&#8243; _module_preset=&#8221;default&#8221; header_font=&#8221;|700|||||||&#8221; header_font_size=&#8221;25px&#8221; text_orientation=&#8221;center&#8221; custom_margin=&#8221;0px||0px||true|false&#8221; custom_padding=&#8221;8px|15px|0px|15px|false|true&#8221; locked=&#8221;off&#8221; global_colors_info=&#8221;{}&#8221;]<\/p>\n<h1>Explore Other Topics<\/h1>\n<p>[\/et_pb_text][et_pb_text _builder_version=&#8221;4.10.7&#8243; _module_preset=&#8221;default&#8221; text_line_height=&#8221;2.2em&#8221; link_font_size=&#8221;16px&#8221; custom_margin=&#8221;||0px||false|false&#8221; custom_padding=&#8221;10px|15px|10px|28px|true|false&#8221; locked=&#8221;off&#8221; global_colors_info=&#8221;{}&#8221;]<\/p>\n<div>\n<div class=\"trr\"><a href=\"https:\/\/stgwebsite.mindspark.in\/wordpress\/math-concepts\/#geometry\" class=\"otherc\">Geometry<\/a><\/div>\n<div class=\"trr\"><a href=\"https:\/\/stgwebsite.mindspark.in\/wordpress\/math-concepts\/#trigonometry\" class=\"otherc\">Trigonometry<\/a><\/div>\n<div class=\"trr\"><a href=\"https:\/\/stgwebsite.mindspark.in\/wordpress\/math-concepts\/#operations\" class=\"otherc\">Operations<\/a><\/div>\n<div class=\"trr\"><a href=\"https:\/\/stgwebsite.mindspark.in\/wordpress\/math-concepts\/#numbers\" class=\"otherc\">Numbers<\/a><\/div>\n<\/div>\n<p>[\/et_pb_text][\/et_pb_column][\/et_pb_row][et_pb_row admin_label=&#8221;Row for space&#8221; _builder_version=&#8221;4.10.6&#8243; _module_preset=&#8221;default&#8221; locked=&#8221;off&#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; 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title_text=&#8221;down-circle&#8221; show_bottom_space=&#8221;off&#8221; align=&#8221;right&#8221; module_class=&#8221;img2&#8243; _builder_version=&#8221;4.9.10&#8243; _module_preset=&#8221;default&#8221; width=&#8221;44px&#8221; height=&#8221;18px&#8221; custom_padding=&#8221;2px||2px||true|false&#8221; global_colors_info=&#8221;{}&#8221;][\/et_pb_image][\/et_pb_column][\/et_pb_row][et_pb_row admin_label=&#8221;FAQ Row&#8221; _builder_version=&#8221;4.9.11&#8243; _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;4.13.1&#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<ol><\/ol>\n<h3><strong>1. What are the features of a convex polygon?<br \/><\/strong><\/h3>\n<p><span style=\"font-weight: 400;\"><strong>Ans: The features of any polygon that is convex are:<\/strong><\/span><\/p>\n<ul>\n<li style=\"font-weight: 400;\" aria-level=\"1\"><span style=\"font-weight: 400;\">It has a minimum of more than 2 sides, vertices and interior angles.<\/span><\/li>\n<li style=\"font-weight: 400;\" aria-level=\"1\"><span style=\"font-weight: 400;\">All interior angles measure less than 180<\/span><span style=\"font-weight: 400;\">\u00b0<\/span><span style=\"font-weight: 400;\">.<\/span><\/li>\n<li style=\"font-weight: 400;\" aria-level=\"1\"><span style=\"font-weight: 400;\">All diagonals lie inside the polygon itself.<\/span><\/li>\n<li style=\"font-weight: 400;\" aria-level=\"1\"><span style=\"font-weight: 400;\">The line joining any two points on the polygon lies wholly inside the polygon.<\/span><\/li>\n<\/ul>\n<p><strong style=\"color: #333333; font-size: 22px;\">2. How is the sum of interior angles of a polygon that is convex in nature determined?<br \/><\/strong><\/p>\n<p><strong>Ans: <\/strong>The sum of interior angles of a convex polygon with \u2018n\u2019 number of sides can be found out by the formula:<strong><br \/><\/strong><b><\/b><\/p>\n<p><span style=\"font-weight: 400;\"><span class=\"katex-eq\" data-katex-display=\"false\">[180\\times (n-2)]^\\circ<\/span>.<\/span>\u00a0<\/p>\n<h3><b>3. What is the main characteristic difference between convex and concave polygon?<br \/><\/b><\/h3>\n<p><b>Ans: <\/b>The main characteristic difference between the convex and concave polygons is that in a concave polygon at some vertices there will be an indent, i.e., the vertex will be pointing inwards whereas in the case of convex all the vertices are outward pointing.<b><br \/><\/b><\/p>\n<p>[\/et_pb_text][\/et_pb_column][\/et_pb_row][\/et_pb_section]<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Meta Description: We can calculate the sum of the terms in a geometric progression using the formula  S = a(1-r^n)\/(1-r) when r < 1 and  S = a(r^n-1)\/(r-1)when r>1<\/p>\n","protected":false},"author":10,"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 - 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