2006 AMC 10B Problems/Problem 8
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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
.
See Also
2006 AMC 10B (Problems • Answer Key • Resources) | ||
Preceded by Problem 7 |
Followed by Problem 9 | |
1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15 • 16 • 17 • 18 • 19 • 20 • 21 • 22 • 23 • 24 • 25 | ||
All AMC 10 Problems and Solutions |
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