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Problem 535

Geometry Difficulty 2.5 Find the answer CEMC Pascal · Canada · 2020

In the diagram, the large square has area 49, the medium square has area 25, and the small square has area 9. The region inside the small square is shaded. The region between the large and medium squares is shaded.

What is the total area of the shaded regions?

$33$ $58$ $45$ $25$ $13$

Your answer

A number or a short expression. Fractions can be typed as 3/2, and spacing doesn't matter.

Official solution

The total area of the shaded region equals the area of the small square (9) plus the area between the large square and medium square.

Since the area of the large square is 49 and the area of the medium square is 25, then the area of the region between these squares is $49 - 25 = 24$ . Therefore, the total area of the shaded region is $9+24=33$ .

Figure for this problem

Source: CEMC, University of Waterloo, licensed CC-BY-NC-4.0. Statement reproduced verbatim; metadata (topic, difficulty, ordering) added by this project.