2000 AMC 8 Problem 6 — Solution | LIVE by Po-Shen Loh

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2000 AMC 8 Problem 6

Attempt Problem 6 of the 2000 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 2000 AMC 8 solutions, or check the answer key.

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

6.

Figure $ABCD$ is a square. Inside this square three smaller squares are drawn with side lengths as labeled. The area of the shaded L-shaped region is

$7$

$10$

$12.5$

$14$

$15$

Answer: A

Concepts:area decomposition square (geometry)

Difficulty rating: 870

Solution:

We can subtract out the areas of the top unit square, the bottom right unit square, and the top right $4 \times 4$ square.

The shaded area in $ABCD$ is therefore $5^2 - 2 \cdot 1^2 - 4^2 = 7.$

Thus, A is the correct answer.

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