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?
First, we need to calculate the area of the original shape.
The original shape consists of a rectangle with dimensions of 8 yards in length and 7 yards in width, so the area of the original shape is:
Area = length x width
Area = 8 yards x 7 yards
Area = 56 square yards
Next, we need to calculate the area of the removed rectangle at the bottom left corner.
The removed rectangle has a width of 3 yards and an unknown length. The remaining width along the bottom right is 3 yards, so the removed rectangle has a length of:
Length = 7 yards - 3 yards - 3 yards
Length = 1 yard
Now, we can calculate the area of the removed rectangle:
Area = length x width
Area = 1 yard x 3 yards
Area = 3 square yards
Finally, we can calculate the area of the swimming pool by subtracting the area of the removed rectangle from the area of the original shape:
Area = 56 square yards - 3 square yards
Area = 53 square yards
Therefore, the area of the swimming pool is 53 square yards.