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Find the area of the regular hexagon

Source: 1970 AHSME Problem 24

March 24, 2014
geometryratioAMC

Problem Statement

An equilateral triangle and a regular hexagon have equal perimeters. If the area of the triangle is 22, then the area of the hexagon is
<spanclass=latexbold>(A)</span>2<spanclass=latexbold>(B)</span>3<spanclass=latexbold>(C)</span>4<spanclass=latexbold>(D)</span>6<spanclass=latexbold>(E)</span>12<span class='latex-bold'>(A) </span>2\qquad<span class='latex-bold'>(B) </span>3\qquad<span class='latex-bold'>(C) </span>4\qquad<span class='latex-bold'>(D) </span>6\qquad <span class='latex-bold'>(E) </span>12