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Area Through Coordinates

Source: 2012 AMC 12 #10

February 23, 2012
geometryanalytic geometryquadraticsconicsellipseAMC

Problem Statement

What is the area of the polygon whose vertices are the points of intersection of the curves x2+y2=25x^2+y^2=25 and (x−4)2+9y2=81(x-4)^2+9y^2=81?
<spanclass=′latex−bold′>(A)</span> 24<spanclass=′latex−bold′>(B)</span> 27<spanclass=′latex−bold′>(C)</span> 36<spanclass=′latex−bold′>(D)</span> 37.5<spanclass=′latex−bold′>(E)</span> 42{{ <span class='latex-bold'>(A)</span>\ 24\qquad<span class='latex-bold'>(B)</span>\ 27\qquad<span class='latex-bold'>(C)</span>\ 36\qquad<span class='latex-bold'>(D)</span>\ 37.5}\qquad<span class='latex-bold'>(E)</span>\ 42}
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