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
30 square yards

56 square yards
56 square yards

65 square yards
65 square yards

44 square yards

1 answer

To find the area of the composite shape (which represents the swimming pool), we will first calculate the area of the whole rectangle and then subtract the area of the removed rectangle.

  1. Area of the original rectangle:

    • Given dimensions: Length = 8 yards, Width = 7 yards.
    • Area = Length × Width = 8 yards × 7 yards = 56 square yards.
  2. Area of the removed rectangle:

    • We know the width of the removed rectangle is 3 yards.
    • The remaining width along the bottom right of the original rectangle is also 3 yards. Since the original width of the rectangle is 7 yards, the width of the removed rectangle can be considered as follows:
      • Total width of the original rectangle = 7 yards.
      • Width remaining on the right = 3 yards.
      • Thus, the width of the removed rectangle = Total width - Width remaining = 7 yards - 3 yards = 4 yards.
    • The height (length) of the removed rectangle is 3 yards (the same as its width).
    • Area of the removed rectangle = Width × Length = 3 yards × 4 yards = 12 square yards.
  3. Remaining area of the swimming pool:

    • Remaining area = Area of the original rectangle - Area of the removed rectangle
    • Remaining area = 56 square yards - 12 square yards = 44 square yards.

The area of the swimming pool is 44 square yards.

So, the correct response is:

44 square yards.