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.

Question

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

44 square yards
44 square yards

56 square yards

Answer 1

To find the area of the swimming pool, we need to figure out the area of the original rectangle and then subtract the area of the removed rectangle.

1. Calculate the area of the large rectangle: The dimensions of the large rectangle are:

   • Length = 8 yards
   • Width = 7 yards

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

2. Determine the dimensions of the removed rectangle: The removed rectangle is 3 yards wide, and we're given that the remaining width along the bottom right is also 3 yards. This means the left over width on the bottom side of the large rectangle is:

   • Total width of the large rectangle = 7 yards
   • Width of the removed rectangle = 3 yards
   • Remaining width after removal = 7 yards - 3 yards = 4 yards

   This means that the width of the removed rectangle must be 3 yards, and the length must be calculated:

   • Since the entire width of the large rectangle is 7 yards and the right side (after the removed rectangle) has 4 yards left, we infer that the length of the removed rectangle is also 4 yards.

3. Calculate the area of the removed rectangle: Area of the removed rectangle = Width × Length = 3 yards × 4 yards = 12 square yards.

4. Calculate the area of the swimming pool: Area of the swimming pool = Area of the large rectangle - Area of the removed rectangle = 56 square yards - 12 square yards = 44 square yards.

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

So the correct response is:

44 square yards.