Area of Composite Figures Quick Check
3 of 53 of 5 Items
Question
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
44 square yards
44 square yards
56 square yards
56 square yards
65 square yards
65 square yards
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To find the area of the swimming pool, we need to find the area of the original rectangle and subtract the area of the rectangle that was removed.
The area of the original rectangle is the length multiplied by the width:
8 yards * 7 yards = 56 square yards.
The area of the rectangle that was removed is also found by multiplying the length by the width:
3 yards * unknown length = 3 yards * unknown length.
Since the width along the bottom right is also 3 yards, we can set up the equation:
7 yards - (3 yards + 3 yards) = unknown length.
Simplifying the equation gives us:
7 yards - 6 yards = unknown length.
So, the unknown length is 1 yard.
Therefore, the area of the rectangle that was removed is:
3 yards * 1 yard = 3 square yards.
To find the area of the swimming pool, we subtract the area of the removed rectangle from the area of the original rectangle:
56 square yards - 3 square yards = 53 square yards.
Therefore, the area of the swimming pool is 53 square yards.