{"id":3634,"date":"2021-11-11T05:57:06","date_gmt":"2021-11-11T05:57:06","guid":{"rendered":"https:\/\/stgwebsite.mindspark.in\/wordpress\/?page_id=3634"},"modified":"2021-11-11T05:57:41","modified_gmt":"2021-11-11T05:57:41","slug":"sample-article-for-format","status":"publish","type":"page","link":"https:\/\/stgwebsite.mindspark.in\/studymaterial\/math-concepts\/sample-article-for-format\/","title":{"rendered":"Sample Article for format"},"content":{"rendered":"

[et_pb_section fb_built=”1″ admin_label=”Section” module_class=”mainsec” _builder_version=”4.10.4″ _module_preset=”default” background_color=”#e0f2fd” z_index=”1″ custom_padding=”5px||5px||true|false” locked=”off” collapsed=”off” global_colors_info=”{}”][et_pb_row column_structure=”3_5,2_5″ custom_padding_last_edited=”on|phone” _builder_version=”4.10.8″ _module_preset=”default” background_color=”#FFFFFF” width=”100%” max_width=”1310px” custom_padding=”|51px|40px|51px|false|true” custom_padding_tablet=”” custom_padding_phone=”|40px|30px|40px|false|true” border_radii=”on|10px|10px|10px|10px” global_colors_info=”{}”][et_pb_column type=”3_5″ admin_label=”Column L” _builder_version=”4.9.10″ _module_preset=”default” global_colors_info=”{}”][et_pb_text admin_label=”Acute Angles
\n” _builder_version=”4.11.3″ _module_preset=”default” header_font=”|700|||||||” header_text_align=”left” header_font_size=”50px” header_line_height=”1.18em” custom_padding=”|0px||4px|false|false” header_font_size_tablet=”” header_font_size_phone=”35px” header_font_size_last_edited=”on|phone” global_colors_info=”{}”]<\/p>\n

Sample Article for format<\/strong><\/h1>\n

[\/et_pb_text][et_pb_text admin_label=”Text” _builder_version=”4.11.3″ _module_preset=”default” text_font_size=”16px” header_2_font=”|600|||||||” header_2_text_color=”#a01414″ header_3_font=”|600|||||||” header_3_text_color=”#898989″ custom_padding=”15px|15px||4px|false|false” global_colors_info=”{}”]<\/p>\n

Calculating the area of a square with diagonals<\/strong><\/h2>\n

The area of a square is the number of unit squares that can be fit into the square completely. To calculate the area of the square, the length and the breadth of the square are multiplied and the resulting product is the area of the square. However, we know that in a square the length and the breadth are the same, and hence the area of the square is a2<\/sup> sq units, where a = length of any of the sides of the square. However, sometimes the length of any side of the square might not be known and only the length of the diagonal of the square is made available. The length of the diagonals of a square is equal.<\/p>\n

In this article, we will learn the formula to calculate the area of the square when the length of its diagonals is given, understand how that formula is derived, and go through some solved illustrations and examples. \u00a0<\/sup><\/p>\n

Formula for calculating the area of a square with diagonals:<\/strong><\/h2>\n

The diagonal of the square is the line that connects any two opposite vertices of the square. The area of a square when only the diagonals are available = \u00a0(1\/2) x d2<\/sup> sq units<\/p>\n

Where d is the length of the diagonal.<\/p>\n

Derivation<\/strong><\/h3>\n

To understand the derivation of the formula, we must first remember the following<\/p>\n

    \n
  1. All the sides of the square are equal and are perpendicular to their adjacent sides<\/li>\n
  2. According to the Pythagoras theorem, (hypotenuse)2 <\/sup>= (base)2<\/sup> + (perpendicular side)2<\/sup><\/li>\n<\/ol>\n

    \u00a0<\/sup><\/p>\n

    Now, in the above square ABCD, let us say the length of the diagonal BD is d and the length of the sides is \u2018a\u2019.\u00a0 We can see that DC is perpendicular to BC and that \u2206 BCD is a right-angle triangle.<\/p>\n

    From Pythagoras theorem, we know that (hypotenuse)2 <\/sup>= (base)2<\/sup> + (perpendicular side)2<\/sup><\/p>\n

    So, BD2 <\/sup>= BC2 <\/sup>+ DC2<\/sup><\/p>\n

    i.e d2<\/sup> = a2 <\/sup>+ a2<\/sup><\/p>\n

    d2<\/sup> = 2a2<\/sup><\/p>\n

    (1\/2) x d2<\/sup> = a2<\/sup><\/p>\n

    Solved Examples<\/strong><\/h3>\n
      \n
    1. Find the area of the square ABCD where the length of diagonal BD = 37 cm.<\/li>\n<\/ol>\n

      Solution:<\/strong><\/p>\n

      We know that the area of the square where only the length of the diagonal is given is equal to \u00a0(1\/2) x d2 <\/sup>where d is the length of the diagonal.<\/p>\n

      So, the area of square ABCD\u00a0 = \u00a0(1\/2) \u00a0x 372 <\/sup>cm2<\/sup><\/p>\n

      \u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 \u00a0\u00a0\u00a0 <\/sup>= 684.5 cm2<\/sup><\/p>\n

      \u00a0<\/sup><\/p>\n

        \n
      1. Find the side and the area of the square PQRS when the diagonal is 17 cm.<\/li>\n<\/ol>\n

        Solution:<\/strong><\/p>\n

        We know from Pythagorean theorem, (hypotenuse)2 <\/sup>= (base)2<\/sup> + (perpendicular side)2<\/sup><\/p>\n

        If the side of the square is a cm, then<\/p>\n

        172<\/sup> = a2<\/sup> + a2<\/sup><\/p>\n

        2a2<\/sup> = 172<\/sup><\/p>\n

        a2<\/sup> =\u00a0 \u00a0(1\/2) x 289<\/p>\n

        a = \u221a144.5<\/p>\n

        a = side = 12.02 cm<\/strong><\/p>\n

        Now that we know that the side = 12.02 cm, area of the square PQRS = 12.02 X 12.02 = 144.5 cm2<\/sup><\/p>\n

          \n
        1. Find the diagonal if the sides of the square are 7 cm.<\/li>\n<\/ol>\n

          We know from Pythagoras theorem, (hypotenuse)2 <\/sup>= (base)2<\/sup> + (perpendicular side)2<\/sup><\/p>\n

          We know that in the given square, base = perpendicular side = 7 cm.<\/p>\n

          Hence, by substituting the above figures in the pythagoras theorem,<\/p>\n

          d2<\/sup> = 72<\/sup> + 72<\/sup><\/p>\n

          d2<\/sup> =2x 72<\/sup><\/p>\n

          d =\u00a0 \u221a98<\/p>\n

          d = 9.89 cm[\/et_pb_text][et_pb_text disabled_on=”on|on|on” admin_label=”Sample Questions
          \n” _builder_version=”4.10.8″ _module_preset=”default” header_font=”|700|||||||” header_font_size=”28px” custom_padding=”|0px||4px|false|false” disabled=”on” global_colors_info=”{}”]<\/p>\n

          Practice Multiple Choice Questions<\/h1>\n

          [\/et_pb_text][et_pb_text disabled_on=”on|on|on” admin_label=”Question 1″ _builder_version=”4.10.8″ _module_preset=”default” background_color=”#FFFFFF” custom_padding=”25px|25px|25px|25px|true|true” border_radii=”on|15px|15px|15px|15px” border_width_all=”2px” border_color_all=”#000000″ border_width_top=”4px” border_color_top=”#E02B20″ disabled=”on” global_colors_info=”{}”]<\/p>\n

          \n
          \n

          Questions<\/strong><\/p>\n

            \n
          1. \u00a0 <\/span>Find the area of the square ABCD where the length of diagonal BD = 37 cm.<\/span><\/li>\n<\/ol>\n

            Solution:<\/b><\/p>\n

            We know that the area of the square where only the length of the diagonal is given is equal to<\/span>\u00a0 1\u00a0 <\/span>2<\/span>x d<\/span>2 <\/span>where d is the length of the diagonal.<\/span><\/p>\n

            So, the area of square ABCD \u00a0 <\/span> = <\/span>\u00a0 1\u00a0 <\/span>2<\/span> x 37<\/span>2 <\/span>cm<\/span>2<\/span>\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0\u00a0<\/span> = 684.5 cm<\/span>2<\/span><\/p>\n

              \n
            1. Find the side and the area of the square PQRS when the diagonal is 17 cm.<\/span><\/li>\n<\/ol>\n

              Solution:<\/b><\/p>\n

              We know from Pythagorean theorem, (hypotenuse)<\/span>2 <\/span>= (base)<\/span>2<\/span> + (perpendicular side)<\/span>2<\/span><\/p>\n

              If the side of the square is a cm, then<\/span><\/p>\n

              17<\/span>2<\/span> = a<\/span>2<\/span> + a<\/span>2<\/span><\/p>\n

              2a<\/span>2<\/span> = 17<\/span>2<\/span><\/p>\n

              a<\/span>2<\/span> = \u00a0 <\/span>\u00a0 1\u00a0 <\/span>2<\/span>x 289\u00a0\u00a0<\/span><\/p>\n

              a = <\/span>\u221a<\/span>144.5<\/span><\/p>\n

              a = side = 12.02 cm<\/b><\/p>\n

              Now that we know that the side = 12.02 cm, area of the square PQRS = 12.02 X 12.02 = 144.5 cm<\/span>2<\/span>\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0<\/span><\/p>\n

                \n
              1. Find the diagonal if the sides of the square are 7 cm.<\/span><\/li>\n<\/ol>\n

                Solution:<\/strong><\/p>\n

                We know from Pythagoras theorem, (hypotenuse)<\/span>2 <\/span>= (base)<\/span>2<\/span> + (perpendicular side)<\/span>2<\/span><\/p>\n

                We know that in the given square, base = perpendicular side = 7 cm.<\/span><\/p>\n

                Hence, by substituting the above figures in the pythagoras theorem,<\/span><\/p>\n

                d<\/span>2<\/span> = 7<\/span>2<\/span> + 7<\/span>2<\/span><\/p>\n

                d<\/span>2<\/span> =2x 7<\/span>2<\/span>\u00a0<\/span><\/p>\n

                d =\u00a0 <\/span>\u221a<\/span>98<\/span><\/p>\n

                d = 9.89 cm<\/span><\/p>\n<\/div>\n<\/div>\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” locked=”off” 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
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                Explore Other Topics<\/h1>\n

                [\/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

                \n
                Geometry<\/a><\/div>\n
                Trigonometry<\/a><\/div>\n
                Operations<\/a><\/div>\n
                Numbers<\/a><\/div>\n<\/div>\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

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                Ready to get started ?<\/p>\n<\/div>\n

                \n

                Start Free Trial<\/a><\/p>\n<\/div>\n<\/div>\n<\/div>\n

                [\/et_pb_text][et_pb_image src=”https:\/\/stgwebsite.mindspark.in\/wordpress\/wp-content\/uploads\/2021\/08\/down-circle.png” title_text=”down-circle” show_bottom_space=”off” align=”right” module_class=”img2″ _builder_version=”4.9.10″ _module_preset=”default” width=”44px” height=”18px” custom_padding=”2px||2px||true|false” global_colors_info=”{}”][\/et_pb_image][\/et_pb_column][\/et_pb_row][et_pb_row admin_label=”FAQ Row” _builder_version=”4.9.11″ _module_preset=”default” width=”100%” max_width=”1310px” custom_padding=”|40px||40px|false|true” global_colors_info=”{}”][et_pb_column type=”4_4″ _builder_version=”4.9.11″ _module_preset=”default” global_colors_info=”{}”][et_pb_text admin_label=”FAQ” module_class=”faqstyl” _builder_version=”4.11.3″ _module_preset=”default” text_font_size=”16px” header_font=”|700|||||||” header_text_align=”center” header_line_height=”2.5em” background_color=”#dbedc6″ max_width=”80%” module_alignment=”center” custom_margin=”||||false|false” custom_padding=”30px|25px|30px|25px|true|true” border_radii=”on|10px|10px|10px|10px” global_colors_info=”{}”]<\/p>\n

                Frequently Asked Questions\u00a0<\/span><\/span><\/h1>\n

                1.<\/strong> How to find the area of the square with the diagonal given?<\/span><\/p>\n

                Ans:<\/strong> The area of a square where only the diagonal is given can be calculated used the formula\u00a0 a<\/span>2<\/sup><\/span> = <\/span>\u00a0 \u00a0(1\/2) <\/span>x d<\/span>2<\/sup><\/span><\/p>\n

                2.<\/strong> How to find the side of the square with only the diagonal given?<\/span><\/p>\n

                Ans:<\/strong> We can calculate the side when the diagonal is given using the Pythagorean theorem or by using the formula side<\/span> =<\/span> \u00a0(1\/\u221a2) <\/span>x diagonal<\/span><\/p>\n

                3.<\/strong> How to find the length of the diagonal of the square?<\/span><\/p>\n

                Ans:<\/strong> We can calculate the length of the diagonal by considering the diagonal as the hypotenuse and the sides of the square as the base and the perpendicular side of a right-angled triangle. We can then use the Pythagorean theorem to calculate the length of the diagonal. Or we can use the formula d= <\/span>\u221a(<\/span>2xa<\/span>2<\/sup><\/span>)<\/span><\/p>\n

                [\/et_pb_text][\/et_pb_column][\/et_pb_row][\/et_pb_section]<\/p>\n","protected":false},"excerpt":{"rendered":"

                The area of a square with only diagonals given can be calculated using the formula a2 = 1 2x d2, where d is the length of the diagonal. <\/p>\n","protected":false},"author":3,"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":"\nSample Article for format - mydomain<\/title>\n<meta name=\"description\" content=\"The area of a square with only diagonals given can be calculated using the formula a2 = ( 1 )\/2x d2, where d is the length of the diagonal.\" \/>\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\/sample-article-for-format\/\" \/>\n<meta property=\"og:locale\" content=\"en_US\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"Sample Article for format - 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