Use the image to answer the question.
A composite shape is drawn with a rectangle and a square. All lines are straight and all corners are marked as right angles. The shape is made with a vertically aligned rectangle 8 yards in length and 7 yards in width. A horizontally aligned rectangle 3 yards wide and of unknown length is removed from the bottom left corner of the original rectangle. The remaining width along the bottom right is 3 yards.
Solve the following problem: A town has a swimming pool shaped as in the diagram.
What is the area of the swimming pool in square yards?
To find the area of the swimming pool, we need to find the area of the original rectangle and subtract the area of the rectangle that was removed.
The area of the original rectangle is length times width, so it is 8 yards x 7 yards = 56 square yards.
The area of the removed rectangle is 3 yards x unknown length = 3x square yards.
Since the remaining width along the bottom right is also 3 yards, the removed rectangle must have been a square, so the unknown length is also 3 yards.
So, the area of the removed rectangle is 3 yards x 3 yards = 9 square yards.
Therefore, the area of the swimming pool is 56 square yards - 9 square yards = 47 square yards.