Problem:
is a regular pentagon. dropped from onto extended and extended, respectively. Let be the center of the pentagon. If , then equals
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Answer Choices:
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Solution:
Let denote the length of a side of the pentagon. We compute the area of in two ways. First (Figure ), it is the sum of the areas of the triangles and . Each of these has base and altitude . Thus the area of the pentagon is . On the other hand (Figure ), the area is the sum of the areas of the triangles and , which have base and altitudes and , respectively. Thus the total area is . Hence and .
