2006 AMC 10B Problems/Problem 8
Revision as of 14:56, 2 August 2006 by Xantos C. Guin (talk | contribs) (added link to previous and next problem)
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