1993 AMC 8 Problem 18

Below is the professionally curated solution for Problem 18 of the 1993 AMC 8, from LIVE by Po-Shen Loh. You can also try the full timed exam, view all 1993 AMC 8 solutions, or check the answer key.

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Concepts:area decomposition triangle area

Difficulty rating: 1090

18.

The rectangle shown has length $AC = 32,$ width $AE = 20,$ and $B$ and $F$ are midpoints of $\overline{AC}$ and $\overline{AE},$ respectively. The area of the quadrilateral $ABDF$ is

$320$

$325$

$330$

$335$

$340$

Solution:

Rectangle $ACDE$ has area $32 \times 20 = 640.$ Triangle $BCD$ has area $\dfrac{16 \times 20}{2} = 160,$ and triangle $DEF$ has area $\dfrac{10 \times 32}{2} = 160.$

The remaining region $ABDF$ has area $640 - (160 + 160) = 320.$

Thus, the correct answer is A .

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