# Problem #2181

 2181 A square of area 40 is inscribed in a semicircle as shown. What is the area of the semicircle? $[asy] unitsize(1cm); defaultpen(.8); draw( (-sqrt(5),0) -- (sqrt(5),0), dashed ); draw( (-1,0)--(-1,2)--(1,2)--(1,0)--cycle ); draw( arc( (0,0), sqrt(5), 0, 180 ) ); [/asy]$ $\mathrm{(A) \ } 20\pi\qquad \mathrm{(B) \ } 25\pi\qquad \mathrm{(C) \ } 30\pi\qquad \mathrm{(D) \ } 40\pi\qquad \mathrm{(E) \ } 50\pi$ This problem is copyrighted by the American Mathematics Competitions.
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• Reduce fractions to lowest terms and enter in the form 7/9.
• Numbers involving pi should be written as 7pi or 7pi/3 as appropriate.
• Square roots should be written as sqrt(3), 5sqrt(5), sqrt(3)/2, or 7sqrt(2)/3 as appropriate.
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