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geometry intermediate

Problem

In the figure, the area of square is . The four smaller squares have sides 1 cm long, either parallel to or coinciding with the sides of the large square. In , , and when is folded over side , point coincides with , the center of square . What is the area of , in square centimeters? Express your answer as a common fraction.
problem
Solution
Let be the midpoint of . Since is isosceles, is an altitude to base . Because coincides with when is folded along , it follows that . Also, , so the area of is .
Final answer
\frac{27}{4}