MathDB
2022 B Individual #18

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April 30, 2022
2022 B Individualgeometry

Problem Statement

Two equilateral triangles are glued, and their opposite vertices are connected. If the larger equilateral triangle has an area of 225225 and the smaller equilateral triangle has an area of 100100, what is the area of the shaded region? [asy] size(4cm); draw((0,0)--(3,0)--(3/2,3sqrt(3)/2)--(0,0)); draw((0,0)--(2,0)--(1,-sqrt(3))--(0,0)); draw((1,-sqrt(3))--(3/2,3sqrt(3)/2)); filldraw((0,0)--(6/5,0)--(3/2,3sqrt(3)/2)--cycle, gray); [/asy]
<spanclass=latexbold>(A)</span>60<spanclass=latexbold>(B)</span>90<spanclass=latexbold>(C)</span>96<spanclass=latexbold>(D)</span>108<spanclass=latexbold>(E)</span>120<span class='latex-bold'>(A) </span>60\qquad<span class='latex-bold'>(B) </span>90\qquad<span class='latex-bold'>(C) </span>96\qquad<span class='latex-bold'>(D) </span>108\qquad<span class='latex-bold'>(E) </span>120