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Geometry Difficulty 2.6 Junior Find the answer Canada

$JKLM$ 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

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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 $64-16=48$ .

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