2013 AMC 8 Problems/Problem 20
Contents
Problem
A rectangle is inscribed in a semicircle with the longer side on the diameter. What is the area of the semicircle?
Solution
A semicircle has symmetry, so the center is exactly at the midpoint of the 2 side on the rectangle, making the radius, by the Pythagorean Theorem, . The area is .
Solution 2
Double the figure to get a square with side length . The circle inscribed around the square has a diameter equal to the diagonal of this square. The diagonal of this square is . The circle’s radius ,therefore, is
The area of the circle is
Finally, the area of the semicircle is , so the answer is .
See Also
2013 AMC 8 (Problems • Answer Key • Resources) | ||
Preceded by Problem 19 |
Followed by Problem 21 | |
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All AJHSME/AMC 8 Problems and Solutions |
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