Question

Four squares of side length $4,$ $7,$ $9,$ and $10$ units are arranged in increasing size order so that their left edges and bottom edges align. The squares alternate shaded and unshaded, as shown in the figure. What is the area of the visible shaded region in square units?

$42$

$45$

$49$

$50$

$52$

Video solution:

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Written solution:

The visible shaded region is the part inside the $10$ by $10$ square but outside the $9$ by $9$ square, together with the part inside the $7$ by $7$ square but outside the $4$ by $4$ square. Its area is $10^2-9^2+7^2-4^2=100-81+49-16=52.$

Thus, E is the correct answer.

2024 AMC 8 Problem 3

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Problem 3 in Other Years