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20

Part of 2013 AMC 8

Problems(1)

2013/8/20/Rectangle inscribed in circle

Source:

11/27/2013
A 1×21\times 2 rectangle is inscribed in a semicircle with longer side on the diameter. What is the area of the semicircle?
<spanclass=′latex−bold′>(A)</span> π2<spanclass=′latex−bold′>(B)</span> 2π3<spanclass=′latex−bold′>(C)</span> π<spanclass=′latex−bold′>(D)</span> 4π3<spanclass=′latex−bold′>(E)</span> 5π3<span class='latex-bold'>(A)</span>\ \frac\pi2 \qquad <span class='latex-bold'>(B)</span>\ \frac{2\pi}3 \qquad <span class='latex-bold'>(C)</span>\ \pi \qquad <span class='latex-bold'>(D)</span>\ \frac{4\pi}3 \qquad <span class='latex-bold'>(E)</span>\ \frac{5\pi}3
geometryrectanglesymmetryanalytic geometryPythagorean TheoremAMC