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Problem 219

Geometry Difficulty 1.4 Multiple choice CEMC Gauss (Grade 8) · Canada · 2024

In the diagram, a square with side length $6$ is partially shaded.

The largest shaded region is a square with side length $3$ . The other two shaded regions are
squares with side lengths $2$ and
$1$ . What is the total area of the
unshaded region?

Pick one

Official solution

The large square with side length $6$ has area $6\times6=36$ .

The shaded squares with side lengths $3$ , $2$
and $1$ , have areas $3\times3=9$ , and $2\times2=4$ , and $1\times1=1$ , respectively.

The total area of the shaded regions is $9+4+1=14$ .

The total area of the unshaded region is equal to the area of the shaded
regions subtracted from the area of the large square, or $36-14=22$ .

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