MathDB
2006 AMC 10 #8

Source:

August 20, 2011
geometryPythagorean Theorem

Problem Statement

A square of area 4040 is inscribed in a semicircle as shown. What is the area of the semicircle?
[asy] defaultpen(linewidth(0.8)); real r=sqrt(50), s=sqrt(10); draw(Arc(origin, r, 0, 180)); draw((r,0)--(-r,0), dashed); draw((s,0)--(s,2*s)--(-s,2*s)--(-s,0));[/asy]
<spanclass=latexbold>(A)</span>20π<spanclass=latexbold>(B)</span>25π<spanclass=latexbold>(C)</span>30π<spanclass=latexbold>(D)</span>40π<spanclass=latexbold>(E)</span>50π <span class='latex-bold'>(A) </span>20\pi\qquad<span class='latex-bold'>(B) </span>25\pi\qquad<span class='latex-bold'>(C) </span>30\pi\qquad<span class='latex-bold'>(D) </span>40\pi\qquad<span class='latex-bold'>(E) </span>50\pi