{"id":3093,"date":"2022-10-28T20:08:00","date_gmt":"2022-10-29T00:08:00","guid":{"rendered":"http:\/\/mathfun4kids.com\/mlog\/?p=3093"},"modified":"2024-10-25T10:54:00","modified_gmt":"2024-10-25T14:54:00","slug":"mathcounts-geometry-exercise-1","status":"publish","type":"post","link":"https:\/\/mathfun4kids.com\/mlog\/?p=3093","title":{"rendered":"MathCounts Geometry Exercise – 1"},"content":{"rendered":"\n
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  1. ________ One rectangle is divided into four smaller rectangles. The areas of three smaller rectangles are $25\\ cm^2$, $20\\ cm^2$, and $30\\ cm^2$ respectively, as shown in the diagram. Find the area of the shaded region (unit: $cm^{2}$)<\/li><\/ol>
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    1. ________ Inside rectangle $ABCD$, $EFGH$ is a square. $AE=10\\ cm$, $GC=7\\ cm$. What is the perimeter of rectangle $ABCD$ in $cm$?<\/li><\/ol>
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      1. ________ Two congruent right triangles overlap each other. $AB=8\\ cm$, $BF=6\\ cm$, and $EF$ is split into two segments, with the length of the top segment as $3\\ cm$. Find the area of the shaded region in $cm^2$.<\/li><\/ol>
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        1. ________ Four congruent rectangles and one smaller square form a bigger square with its area as $144$. If the area of the smaller square is $4$, and $x$ and $y$ are the length and height of the rectangles, then $x=$________ and $y=$________.<\/li><\/ol>
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          1. ________ The area of $\\triangle{EDF}$ is $6\\ cm^{2}$ bigger than the area of $\\triangle{ABE}$. The length and height of rectangle $ABCD$ are $6\\ cm$ and $4\\ cm$ respectively. Find the length of $DF$ in $cm$.<\/li><\/ol>
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            1. ________ $\\triangle{ABC}$ is divided by line $DE$ into two regions, one in black, one in white. If $BD=DC=4$, $BE=2$, $EA=4$, find the area ratio between the black region and the white region. Express your answer as a common fraction.<\/li><\/ol>
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              1. ________ The area of square $ABCD$ is $3\\ cm^{2}$, $M$ is the midpoint of $AD$. Find the area of the shaded region in $cm^{2}$.<\/li><\/ol>
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                1. ________ 3 pieces of congruent square-shaped paper in color red, yellow, and green are placed in a box with a square-shaped bottom. They overlap with each other. If the visible areas of the red, yellow, and green paper are $20$, $14$, and $10$ respectively, find the area of the square-shaped bottom of the box.<\/li><\/ol>
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                  1. ________ In trapezoid $ABCD$, $AD=3\\ cm$, $BC=9\\ cm$. The area of $\\triangle{ABO}$ is $12\\ cm^2$. Find the area of trapezoid $ABCD$ in $cm^2$.<\/li><\/ol>
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                    1. ________ The side length of the larger square is $5\\ cm$. The side length of the smaller square is $3\\ cm$. Find the area of the shaded region in $cm^2$. <\/li><\/ol>
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                      25 20 30 ________ One rectangle is divided into four smaller rectangles. The areas of three smaller rectangles are $25\\ cm^2$, $20\\ cm^2$, and $30\\ cm^2$ respectively, as shown in the diagram. Find the area of the shaded region (unit: … Continue reading →<\/span><\/a><\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"inline_featured_image":false},"categories":[9,18,11],"tags":[],"_links":{"self":[{"href":"https:\/\/mathfun4kids.com\/mlog\/index.php?rest_route=\/wp\/v2\/posts\/3093"}],"collection":[{"href":"https:\/\/mathfun4kids.com\/mlog\/index.php?rest_route=\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/mathfun4kids.com\/mlog\/index.php?rest_route=\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/mathfun4kids.com\/mlog\/index.php?rest_route=\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/mathfun4kids.com\/mlog\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=3093"}],"version-history":[{"count":178,"href":"https:\/\/mathfun4kids.com\/mlog\/index.php?rest_route=\/wp\/v2\/posts\/3093\/revisions"}],"predecessor-version":[{"id":4598,"href":"https:\/\/mathfun4kids.com\/mlog\/index.php?rest_route=\/wp\/v2\/posts\/3093\/revisions\/4598"}],"wp:attachment":[{"href":"https:\/\/mathfun4kids.com\/mlog\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=3093"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/mathfun4kids.com\/mlog\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=3093"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/mathfun4kids.com\/mlog\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=3093"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}