Use the image to answer the question.
An illustration shows a parallelogram that is divided into four equal sections by a horizontal and a vertical line intersecting at the center. Measurements are labeled on the bottom first section as follows: The base is labeled 8 inches and left side is 5 inches. The perpendicular height from the top left vertex to the base is 4 inches. The height is drawn in dashed line.
To cover a garden path, a landscape designer plans to cover a walkway with parallelogram-shaped paving stones. Construct a rectangle to find the area covered by 4 paving stones. What is the area in square inches?
(1 point)
Responses
160 square inches
160 square inches
128 square inches
128 square inches
52 square inches
52 square inches
40 square inches
160 square inches
how do you know?
To find the area covered by 4 paving stones, we need to construct a rectangle that includes all 4 parallelograms. The base of each parallelogram is 8 inches and the height is 4 inches. So, the area of each parallelogram is 8 x 4 = 32 square inches. Therefore, the area of 4 parallelograms is 4 x 32 = 128 square inches. Since the parallelograms form a rectangle, the area of the rectangle is also 128 square inches.
what is the exact answer, though? 160 sq in or 128 sq in?
The exact answer is 128 square inches.
To find the area covered by four parallelogram-shaped paving stones, we need to construct a rectangle using those paving stones.
First, let's calculate the total width of the rectangle. Since the base of each paving stone is 8 inches, and we have four paving stones, the total width is 8 x 4 = 32 inches.
Next, let's calculate the total height of the rectangle. The perpendicular height from the top left vertex to the base is 4 inches. Since the parallelogram is divided into four equal sections, the total height is 4 x 4 = 16 inches.
Now, we can find the area of the rectangle by multiplying the width by the height: 32 x 16 = 512 square inches.
Therefore, the area covered by four parallelogram-shaped paving stones is 512 square inches.