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### Find the Area of the Quadrilateral

```Date: 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

[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/
```
Associated Topics:
College Triangles and Other Polygons
High School Triangles and Other Polygons

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