MathDB
Squares and Diagonals

Source: 2018 AMC 8 #22

November 20, 2018
AMC 8geometry2018 AMC 8

Problem Statement

Point EE is the midpoint of side CD\overline{CD} in square ABCD,ABCD, and BE\overline{BE} meets diagonal AC\overline{AC} at F.F. The area of quadrilateral AFEDAFED is 45.45. What is the area of ABCD?ABCD?
[asy] size(5cm); draw((0,0)--(6,0)--(6,6)--(0,6)--cycle); draw((0,6)--(6,0)); draw((3,0)--(6,6)); label("AA",(0,6),NW); label("BB",(6,6),NE); label("CC",(6,0),SE); label("DD",(0,0),SW); label("EE",(3,0),S); label("FF",(4,2),E); [/asy]
<spanclass=latexbold>(A)</span>100<spanclass=latexbold>(B)</span>108<spanclass=latexbold>(C)</span>120<spanclass=latexbold>(D)</span>135<spanclass=latexbold>(E)</span>144<span class='latex-bold'>(A) </span> 100 \qquad <span class='latex-bold'>(B) </span> 108 \qquad <span class='latex-bold'>(C) </span> 120 \qquad <span class='latex-bold'>(D) </span> 135 \qquad <span class='latex-bold'>(E) </span> 144