1988 AMC 8 Problem 17

Attempt Problem 17 of the 1988 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 1988 AMC 8 solutions, or check the answer key.

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17.

The shaded area is formed by two intersecting perpendicular rectangles, with dimensions as shown. Its area, in square units, is

2323

3838

4444

4646

unable to be determined from the information given

Answer: B
Concepts:areainclusion-exclusion

Difficulty rating: 960

Solution:

The horizontal rectangle has area 10×2=20,10 \times 2 = 20, and the vertical rectangle has area 3×8=24.3 \times 8 = 24. Their overlap, a 3×23 \times 2 rectangle, has area 6.6.

Adding the two rectangles counts the overlap twice, so the shaded area is 20+246=38.20 + 24 - 6 = 38.

Thus, the correct answer is B .

← Problem 16#16Full ExamProblem 18#18 →

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