Use the image to answer the question.
An illustration shows a trapezoid with shorter base of length 36 and the opposite longer side of length 48. The legs on the left and right sides are of length 21. The perpendicular height from the bottom left vertex to the longer side is 18. The length between the top left vertex of the longer side and the point where the height meets the longer side is labeled 6. The height is shown in a dashed line.
Compose a rectangle to help find the area of a trapezoid-shaped tabletop in square inches. What is the area of the tabletop?
(1 point)
Responses
756 square inches
756 square inches
648 square inches
648 square inches
864 square inches
864 square inches
882 square inches
882 square inches
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To find the area of the trapezoid-shaped tabletop, we need to find the area of the rectangle that can be composed using the trapezoid's height and the length between the top left vertex and where the height meets the longer side.
The area of the rectangle is length x width. The length of the rectangle is the trapezoid's height, which is 18 inches, and the width is the length between the top left vertex and where the height meets the longer side, which is 6 inches.
So, the area of the rectangle is 18 x 6 = 108 square inches.
Since the area of the rectangle is equivalent to half of the trapezoid's area, we can find the total area of the trapezoid by doubling the area of the rectangle.
Thus, the area of the trapezoid-shaped tabletop is 108 x 2 = 216 square inches.