# 1979 AHSME Problems/Problem 1

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## Problem 1 $[asy] draw((-2,1)--(2,1)--(2,-1)--(-2,-1)--cycle); draw((0,0)--(0,-1)--(-2,-1)--(-2,0)--cycle); label("F",(0,0),E); label("A",(-2,1),W); label("B",(2,1),E); label("C", (2,-1),E); label("D",(-2,-1),WSW); label("E",(-2,0),W); label("G",(0,-1),S); //Credit to TheMaskedMagician for the diagram [/asy]$

If rectangle ABCD has area 72 square meters and E and G are the midpoints of sides AD and CD, respectively, then the area of rectangle DEFG in square meters is $\textbf{(A) }8\qquad \textbf{(B) }9\qquad \textbf{(C) }12\qquad \textbf{(D) }18\qquad \textbf{(E) }24$

## Solution

Solution by e_power_pi_times_i

Since the dimensions of $DEFG$ are half of the dimensions of $ABCD$, the area of $DEFG$ is $\dfrac{1}{2}\cdot\dfrac{1}{2}$ of $ABCD$, so the area of $ABCD$ is $\dfrac{1}{4}\cdot72 = \boxed{\textbf{(D) } 18}$.

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