Question

In the figure below, $ABCD$ is a rectangle with sides of length $AB = 5$ inches and $AD = 3$ inches. Rectangle $ABCD$ is rotated $90^\circ$ clockwise around the midpoint of side $DC$ to give a second rectangle. What is the total area, in square inches, covered by the two overlapping rectangles?

$21$

$22.25$

$23$

$23.75$

$25$

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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 $5 \times 3 = 15.$

Their overlap is a square that has side length $2.5,$ and so its area is $2.5^2 = 6.25.$

Therefore, the total area is $15 + 15 - 6.25 = 23.75,$ which is choice D.

2025 AMC 8 Problem 10

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Problem 10 in Other Years