1961 AHSME Problems/Problem 32
Problem
A regular polygon of sides is inscribed in a circle of radius . The area of the polygon is . Then equals:
Solution
Note that the distance from the center of the circle to each of the vertices of the inscribed regular polygon equals the radius . Since each side of a regular polygon is the same length, all the angles between the two lines from the center to the two vertices of a side is the same.
That means each of these angles between the two lines from the center to the two vertices of a side equals degrees. Thus, the area of the polygon is Dividing both sides by yields Multiply both sides by to get At this point, use trial-and-error for each of the answer choices. When checking , the equation results in , which is correct. Thus, the answer is .
See Also
1961 AHSC (Problems • Answer Key • Resources) | ||
Preceded by Problem 31 |
Followed by Problem 33 | |
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