1993 AMC 8 Problem 18

Attempt Problem 18 of the 1993 AMC 8 below, then check your answer against the professionally curated solution 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.

All problems are used with official legal permission of the Mathematical Association of America (MAA).

18.

The rectangle shown has length AC=32,AC = 32, width AE=20,AE = 20, and BB and FF are midpoints of AC‾\overline{AC} and AE‾,\overline{AE}, respectively. The area of the quadrilateral ABDFABDF is
320320
325325
330330
335335
340340
Answer: A
Concepts:area decompositiontriangle area
Small hint:
The rectangle ACDEACDE has area 32×20;32 \times 20; remove the parts outside ABDFABDF
Big hint:
Subtract triangle BCDBCD and triangle DEFDEF from the full rectangle
Solution:
Rectangle ACDEACDE has area 32×20=640.32 \times 20 = 640. Triangle BCDBCD has area 16×202=160,\dfrac{16 \times 20}{2} = 160, and triangle DEFDEF has area 10×322=160.\dfrac{10 \times 32}{2} = 160.
The remaining region ABDFABDF has area 640−(160+160)=320.640 - (160 + 160) = 320.
Thus, the correct answer is A .
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