Difference between revisions of "2016 AMC 10B Problems/Problem 21"

(Created page with "==Problem== What is the area of the region enclosed by the graph of the equation <math>x^2+y^2=|x|+|y|?</math> <math>(A) \pi+\sqrt{2} (B) \pi+2 (C) \pi+2\sqrt{2} (D) 2\pi+\s...")
 
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What is the area of the region enclosed by the graph of the equation <math>x^2+y^2=|x|+|y|?</math>
 
What is the area of the region enclosed by the graph of the equation <math>x^2+y^2=|x|+|y|?</math>
  
<math>(A) \pi+\sqrt{2} (B) \pi+2 (C) \pi+2\sqrt{2} (D) 2\pi+\sqrt{2} (E) 2\pi+2\sqrt{2}</math>
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<math>\textbf{(A)}\ \pi+\sqrt{2}\qquad\textbf{(B)}\ \pi+2\qquad\textbf{(C)}\ \pi+2\sqrt{2}\qquad\textbf{(D)}\ 2\pi+\sqrt{2}\qquad\textbf{(E)}\ 2\pi+2\sqrt{2}</math>

Revision as of 10:07, 21 February 2016

Problem

What is the area of the region enclosed by the graph of the equation $x^2+y^2=|x|+|y|?$

$\textbf{(A)}\ \pi+\sqrt{2}\qquad\textbf{(B)}\ \pi+2\qquad\textbf{(C)}\ \pi+2\sqrt{2}\qquad\textbf{(D)}\ 2\pi+\sqrt{2}\qquad\textbf{(E)}\ 2\pi+2\sqrt{2}$