Problem:
Point is the center of the regular octagon , and is the midpoint of side . What fraction of the area of the octagon is shaded?
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Answer Choices:
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Solution:
The octagon can be divided into congruent triangles, of which are , and . The area of is half the area of one of these, so the fraction of the area of the octagon that is shaded is .
Answer: .
The problems on this page are the property of the MAA's American Mathematics Competitions