1989 AMC 8 Problem 15

Attempt Problem 15 of the 1989 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 1989 AMC 8 solutions, or check the answer key.

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15.

In parallelogram $ABCD$ shown, what is the area of the shaded region $BEDC?$

$24$

$48$

$60$

$64$

$80$

Answer: D

Concepts:parallelogram area decomposition

Difficulty rating: 860

Solution:

The parallelogram has base $10$ and height $8,$ so its area is $10 \times 8 = 80.$

The unshaded triangle $ABE$ has base $AE = AD - ED = 10 - 6 = 4$ and height $8,$ so its area is $\frac{1}{2} \times 4 \times 8 = 16.$ The shaded area is $80 - 16 = 64.$

Thus, the correct answer is D .

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