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CEMC Gauss (Grade 7), 2020

Geometry Difficulty 1.4 Junior Find the answer Canada

Points $P(15,55)$ , $Q(26,55)$ and $R(26,35)$ are three vertices of rectangle $PQRS$ .

The area of this rectangle is

Pick one

Solution

The $y$ -coordinates of points $P(15,55)$ and $Q(26,55)$ are equal.

Therefore, the distance between $P$ and $Q$ is equal to the positive difference between their $x$ -coordinates, or $26-15=11$ .

Similarly, the $x$ -coordinates of points $R(26,35)$ and $Q(26,55)$ are equal.

Therefore, the distance between $R$ and $Q$ is equal to the positive difference between their $y$ -coordinates, or $55-35=20$ .
Since $PQ=11$ and $RQ=20$ , the area of rectangle $PQRS$ is $11\times20=220$ .

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