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Problem 410

Geometry Difficulty 2.6 Multiple choice CEMC Gauss (Grade 7) · Canada · 2013

$JKLM$ is a square and $PQRS$ is a rectangle.

If $JK$ is parallel to $PQ$ , $JK=8$ and $PS=2$ , then the total area of the shaded regions is

Pick one

Official solution

The total area of the shaded regions is the difference between the area of square $JKLM$ and the area of the portion of rectangle $PQRS$ that overlaps $JKLM$ .

Since $JK=8$ , then the area of square $JKLM$ is $8\times8$ or 64.

Since $JK$ is parallel to $PQ$ , then the portion of $PQRS$ that overlaps $JKLM$ is a rectangle, and has length equal to $JK$ or 8, and width equal to $PS$ or 2.

So the area of the portion of $PQRS$ that overlaps $JKLM$ is $8\times2=16$ .
Therefore the total area of the shaded regions is $64-16=48$ .

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