2006 AMC 10A Problems/Problem 17
Problem
In rectangle , points and trisect , and points and trisect . In addition, . What is the area of quadrilateral shown in the figure?
Contents
[hide]Solution
Solution 1
It is not difficult to see by symmetry that is a square. Draw . Clearly . Then is isosceles, and is a . Hence , and .
There are many different similar ways to come to the same conclusion using different 45-45-90 triangles.
Solution 2
Draw the lines as shown above, and count the squares. There are 12, so we have .
See Also
2006 AMC 10A (Problems • Answer Key • Resources) | ||
Preceded by Problem 16 |
Followed by Problem 18 | |
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All AMC 10 Problems and Solutions |