Problem

2018 AMC 8 Problem 22

Point E is the midpoint of side \overline{CD} in square ABCD, and \overline{BE} meets diagonal \overline{AC} at F. The area of quadrilateral AFED is 45. What is the area of 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("$A$",(0,6),NW); label("$B$",(6,6),NE); label("$C$",(6,0),SE); label("$D$",(0,0),SW); label("$E$",(3,0),S); label("$F$",(4,2),E); [/asy]

\textbf{(A) } 100 \qquad \textbf{(B) } 108 \qquad \textbf{(C) } 120 \qquad \textbf{(D) } 135 \qquad \textbf{(E) } 144

Full credit goes to MAA for authoring these problems. These problems were taken on the AOPS website.


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Category: AMC 8
Points: 2
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