Problem:
Points and are midpoints of the sides of the larger square. If the larger square has area , what is the area of the smaller square?
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Answer Choices:
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Solution:
Divide the larger square into congruent triangles, as shown, of which make up the smaller square.
The area of the smaller square is or of the area of the larger square, so the area of the smaller square is equal to .
Answer: .
The problems on this page are the property of the MAA's American Mathematics Competitions