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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

65 square yards
65 square yards

56 square yards
56 square yards

44 square yards
44 square yards

30 square yards
30 square yards

Answer 1

To find the area of the swimming pool, we will first calculate the area of the original rectangle and then subtract the area of the smaller rectangle that was removed.

1. Calculate the area of the original rectangle:

   • Length = 8 yards
   • Width = 7 yards
   • Area = Length × Width = 8 × 7 = 56 square yards.

2. Identify the dimensions of the smaller rectangle:

   • The width of the smaller rectangle is given as 3 yards.
   • The remaining width along the bottom right is also 3 yards, meaning the entire remaining width at the bottom of the rectangle is 7 yards (3 yards from the smaller rectangle and 3 yards from the side).
   • Therefore, the length of the smaller rectangle can be calculated:
     • Length of the smaller rectangle = Total width of the original rectangle - Width of the smaller rectangle = 7 - 3 = 4 yards.

3. Calculate the area of the smaller rectangle:

   • Width = 3 yards
   • Length = 4 yards
   • Area of the smaller rectangle = Width × Length = 3 × 4 = 12 square yards.

4. Calculate the area of the swimming pool:

   • Area of swimming pool = Area of original rectangle - Area of smaller rectangle
   • Area = 56 - 12 = 44 square yards.

Thus, the area of the swimming pool is 44 square yards.

The correct response is: 44 square yards.