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?
(1 point)
Responses
30 square yards
65 square yards
56 square yards
44 square yards
To find the area of the swimming pool, we need to subtract the area of the horizontally aligned rectangle from the total area of the vertically aligned rectangle.
The total area of the vertically aligned rectangle is 8 yards * 7 yards = 56 square yards.
The area of the horizontally aligned rectangle is 3 yards * unknown length = 3y.
We know that the remaining width along the bottom right is 3 yards, so the length of the horizontally aligned rectangle can be found by subtracting the remaining width from the total width of the vertically aligned rectangle: 7 yards - 3 yards = 4 yards.
So, the area of the horizontally aligned rectangle is 3 yards * 4 yards = 12 square yards.
We can now subtract the area of the horizontally aligned rectangle from the total area of the vertically aligned rectangle: 56 square yards - 12 square yards = 44 square yards.
Therefore, the area of the swimming pool is 44 square yards.