2025 AMC 8 Problem 10
Attempt Problem 10 of the 2025 AMC 8 below, then check your answer against the video solution and professionally curated solution from LIVE by Po-Shen Loh. You can also try the full timed exam, view all 2025 AMC 8 solutions, or check the answer key.
All problems are used with official legal permission of the Mathematical Association of America (MAA).
10.
In the figure below, is a rectangle with sides of length inches and inches. Rectangle is rotated clockwise around the midpoint of side to give a second rectangle. What is the total area, in square inches, covered by the two overlapping rectangles?
Answer: D
Small hint:
Add the two rectangle areas and subtract the overlap
Big hint:
The overlap is a square whose side is half of the -inch side
Video solution:
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Written solution:
The easiest way to solve this problem is using the Inclusion-Exclusion formula. That is: add the areas of the two rectangles, and then subtract the overlapping (square) area.
Each rectangle has area
Their overlap is a square that has side length and so its area is
Therefore, the total area is which is choice D.
Problem 10 in other years
- 1985 AMC 8
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