Find the Area of the QuadrilateralDate: 05/20/2003 at 00:18:57 From: N. Arun Subject: Geometry Vertex Q of square QRST is at the center of square MNOP. The length of a side of MNOP is 1 and the length of a side of QRST is 2. Side QR intersects OP at X and QT intersects MP at Y. If angle QXP is 60, the area of quadrilateral QXPY is [1] ((3^0.5)/6) [2] 1/3 [3] 1/4 [4] ((2^0.5)/4) I don't know how to calculate the area of a quadrilateral using only the vertex angles. Date: 05/21/2003 at 12:28:09 From: Doctor Peterson Subject: Re: Geometry Thanks for writing to Dr. Math. Here is my version of the figure; since the size of QRST doesn't matter, I only show Q and the edges connected to it: N-------------------------------------------O | | | | | | ---- | | ---- | -X- | ----.| | ----.....| | ---.........| | ----............| | ----................| | Q---------------------A | |\....................| | | \...................| | | \..................| | | \.................| | | \................| | | \...............| | | \..............| | | \.............| | | \............| | | \...........| M---------------------B----------Y----------P \ \ Think about how you can find the areas of triangles QAX and QBY; don't actually calculate them just yet. How would you use those areas to find the area of QXPY? One approach is to compare it with square QAPB. Do you see a very easy way to find the area? - Doctor Peterson, The Math Forum http://mathforum.org/dr.math/ |
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