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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

30 square yards
30 square yards

56 square yards
56 square yards

44 square yards

Answer 1

To find the area of the swimming pool, we first need to determine the dimensions of the original rectangle and the cutout rectangle.

1. The original rectangle has a length of 8 yards and a width of 7 yards.

   • Area of the original rectangle = Length × Width = 8 yards × 7 yards = 56 square yards.

2. A rectangular cutout is removed from the bottom left corner. This cutout is 3 yards wide. We need to determine its length.

   • Since the total width of the original rectangle is 7 yards and the remaining width along the bottom right is also 3 yards, the remaining width of the rectangle on the left must be \(7 - 3 = 4\) yards.
   • This indicates that the cutout rectangle has a width of 3 yards and a length of 4 yards.

3. Now, calculate the area of the cutout rectangle.

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

4. Finally, to find the area of the swimming pool (the area of the remaining shape after the cutout is removed), we subtract the area of the cutout from the area of the original rectangle.

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

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