2006 AMC 10B Problems/Problem 8
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 a side is . The distance between the center of the semicircle and one of the bottom vertices of the square is half the length of the side, which is .
Using the Pythagorean Theorem to find the radius of the semicircle, . So, the area of the semicircle is .
See Also
2006 AMC 10B (Problems • Answer Key • Resources) | ||
Preceded by Problem 7 |
Followed by Problem 9 | |
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