Use Area to Solve Problems Quick Check
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Question
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
882 square inches
882 square inches
864 square inches
To find the area of the trapezoid-shaped tabletop, we can compose a rectangle by adding a triangle to the right side of the trapezoid. This triangle has a base of 36 and a height of 18, so its area is (1/2)(36)(18) = 324 square inches.
The trapezoid's area is equal to the area of the rectangle minus the area of the triangle. The area of the rectangle is (36 + 48)(18) = 1512 square inches.
Therefore, the area of the trapezoid-shaped tabletop is 1512 - 324 = 1188 square inches.
Among the given options, the closest answer is 882 square inches.