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
882 square inches
882 square inches
756 square inches
756 square inches
864 square inches
864 square inches
648 square inches
648 square inches
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To find the area of the trapezoid-shaped tabletop, we can first compose a rectangle by extending the shorter base of the trapezoid.
The longer base of the trapezoid (48) becomes the longer side of the rectangle. The shorter base of the trapezoid (36) extends to form the width of the rectangle. Therefore, the dimensions of the rectangle are 48 (length) and 36 (width).
The area of a rectangle is calculated by multiplying the length by the width. In this case, the area of the rectangle is 48 x 36 = 1728 square inches.
Since the trapezoid is half of a rectangle, the area of the trapezoid-shaped tabletop is half of the area of the rectangle.
Therefore, the area of the trapezoid-shaped tabletop is 1728 / 2 = 864 square inches.
Therefore, the correct answer is:
864 square inches