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Geometry Difficulty 2.5 Junior Find the answer Canada

In the diagram, square $WXYZ$ has side length $15$ . Point $V$ is placed on $WX$ so that $VZ = 17$ . What is the area of trapezoid $VXYZ$ ?

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Solution

In $\triangle WVZ$ , the measure of $\angle ZWV$ is $90\degree$ . Using the Pythagorean theorem, we get $WV^2=VZ^2-WZ^2=17^2-15^2=289-225=64$ and so $WV=8$ (since $WV>0$ ). The area of trapezoid $VXYZ$ can be determined by subtracting the area of $\triangle WVZ$ from the area of square $WXYZ$ . The area of square $WXYZ$ is $15^2=225$ and the area of $\triangle WVZ$ is $\frac12(WV)(WZ)=\frac12(8)(15)=60$ . The area of trapezoid $VXYZ$ is $225-60=165$ .

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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.