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 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