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Finding the area of a nice closed region

Source: AMC 10B #21

February 21, 2016
geometryAMCAMC 10AMC 10 B

Problem Statement

What is the area of the region enclosed by the graph of the equation x2+y2=∣x∣+∣y∣?x^2+y^2=|x|+|y|?
<spanclass=′latex−bold′>(A)</span> π+2<spanclass=′latex−bold′>(B)</span> π+2<spanclass=′latex−bold′>(C)</span> π+22<spanclass=′latex−bold′>(D)</span> 2π+2<spanclass=′latex−bold′>(E)</span> 2π+22<span class='latex-bold'>(A)</span>\ \pi+\sqrt{2} \qquad<span class='latex-bold'>(B)</span>\ \pi+2 \qquad<span class='latex-bold'>(C)</span>\ \pi+2\sqrt{2} \qquad<span class='latex-bold'>(D)</span>\ 2\pi+\sqrt{2} \qquad<span class='latex-bold'>(E)</span>\ 2\pi+2\sqrt{2}
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