CEMC Pascal, 2026

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 $VXYZ$ ?

Pick one

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 $\text{WV gt;0}$ ). 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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