{"id":3138,"date":"2022-11-04T22:22:00","date_gmt":"2022-11-05T02:22:00","guid":{"rendered":"http:\/\/mathfun4kids.com\/mlog\/?p=3138"},"modified":"2024-10-25T10:54:45","modified_gmt":"2024-10-25T14:54:45","slug":"mathcounts-geometry-exercise-2","status":"publish","type":"post","link":"https:\/\/mathfun4kids.com\/mlog\/?p=3138","title":{"rendered":"MathCounts Geometry Exercise – 2"},"content":{"rendered":"\n
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  1. ________ The area of $\\triangle{ABC}$ is $1$. $BD:DC=2:1$, and $E$ is the midpoint of $AC$. $AD$ intersects $BE$ at point $P$. Find the area of quadrilateral $PDCE$.<\/li><\/ol>
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    1. ________ Rectangle $ABCD$ is divided into 4 smaller regions, $K$, $L$, $M$, and $N$, with equal area. If the ratio of the length and the height of rectangular region $K$ is $\\dfrac{3}{2}$, what is the ratio of the length and the height of rectangular region $N$? Express your answer as a common fraction.<\/li><\/ol>
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      1. ________ A rectangle metal sheet is cut into two circles and one smaller rectangle, as shown in shared regions, to form a cylinder-shaped oil container. Find the volume of the oil container in liters. Assume $\\pi=3.14$, and round your answer to the nearest integer.<\/li><\/ol>
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        1. ________ $\\triangle{ABC}$ is right and $AC=3$, $BC=4$, $AB=5$. Then $AC$ is folded to $AB$. Find the area of the shaded region, which is not overlapping with other parts of the original triangle. <\/li><\/ol>
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          1. ________ The area of the right $\\triangle{ABC}$ is $12$. A semi-circle is drawn as shown. The area of the shaded region can be expressed as $a\\pi-b$. Find the value of $a+b$.<\/li><\/ol>
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            1. ________ The area of rectangle $ABCD$ is $36\\ cm^2$. $E$, $F$, and $G$ are midpoint of $AB$, $BC$, and $CD$ respectively. $H$ is on $AD$. Find the area of the shaded region in $cm^2$.<\/li><\/ol>
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              1. ________ The area of $\\triangle{ABC}$ is $10\\ cm^2$. $BA$ is extended to $D$ so that $DB=AB$. $CB$ is extended to $E$ so that $EA=2 AC$. $CB$ extended to $F$ so that $FB=3 BC$. Find the area of $\\triangle{DEF}$ in $cm^2$.<\/li><\/ol>
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                1. ________ The area of square $ABCD$ is $900\\ cm^2$. $E$ is the midpoint of $CD$. $F$ is the midpoint of $BC$. $BE$ intersects with $DF$ at $M$, with $AF$ at $N$. Find the area of $\\triangle{MNF}$ in $cm^2$.<\/li><\/ol>
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                  1. ________ $ABCD$ and $CGEF$ are two squares. $CF=3\\ CH$. The area of $CHG$ is $6\\ cm^2$. $E$ Find the area of pentagon $ABGEF$ in $cm^2$.<\/li><\/ol>
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                    1. ________ In trapezoid $ABCD$, $AD\\parallel BC$. $AD=BE=EC$. $BD$ intersects with $AC$ at $O$, and $AE$ at $P$. The area of $\\triangle{AOD}$ is $10\\ cm^2$. Find the area of quadrilateral $OPEC$ in $cm^2$.<\/li><\/ol>
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                      A B C D E P ________ The area of $\\triangle{ABC}$ is $1$. $BD:DC=2:1$, and $E$ is the midpoint of $AC$. $AD$ intersects $BE$ at point $P$. Find the area of quadrilateral $PDCE$. ________ Rectangle $ABCD$ is divided into 4 … 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\/3138"}],"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=3138"}],"version-history":[{"count":66,"href":"https:\/\/mathfun4kids.com\/mlog\/index.php?rest_route=\/wp\/v2\/posts\/3138\/revisions"}],"predecessor-version":[{"id":4597,"href":"https:\/\/mathfun4kids.com\/mlog\/index.php?rest_route=\/wp\/v2\/posts\/3138\/revisions\/4597"}],"wp:attachment":[{"href":"https:\/\/mathfun4kids.com\/mlog\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=3138"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/mathfun4kids.com\/mlog\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=3138"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/mathfun4kids.com\/mlog\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=3138"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}