Difference between revisions of "2006 AMC 10B Problems/Problem 8"
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Revision as of 20:24, 3 August 2006
Problem
A square of area 40 is inscribed in a semicircle as shown. What is the area of the semicircle?
Solution
Since the area of the square is , the length of the side is . The distance between the center of the semicircle and one of the bottom vertecies of the square is half the length of the side, which is .
Using the Pythagorean Theorem to find the square of radius:
So, the area of the semicircle is