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CEMC Gauss (Grade 7), 2026

Geometry Difficulty 2.5 Junior Find the answer Canada

In the diagram, $\triangle PQR$ has base $PQ=8~\text{cm}$ and height $6~\text{cm}$ . $\triangle PST$ has base $PS=4~\text{cm}$ and height $3~\text{cm}$ .

What is the area of the shaded region?

Pick one

Solution

The area of $\triangle PQR$ is
$\dfrac12\times8\text{ cm}\times6\text{ cm}=24\text{ cm}^2$ .
The area of $\triangle PST$ is $\dfrac12\times4\text{ cm}\times3\text{ cm}=6\text{ cm}^2$ .

The area of the shaded region is equal to the area of $\triangle PQR$ minus the area of $\triangle PST$ , which is $24\text{ cm}^2-6\text{ cm}^2=18\text{ cm}^2$ .

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