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Problem 362

Geometry Difficulty 2.5 Multiple choice CEMC Gauss (Grade 7) · Canada · 2026

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

Official 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$.

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