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
648 square inches
648 square inches
882 square inches
882 square inches
864 square inches
864 square inches
756 square inches
756 square inches
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To find the area of the trapezoid-shaped tabletop, we need to first find the area of the rectangle formed by extending the shorter base of the trapezoid to create a rectangle.
The area of the rectangle = base x height
= 48 x 18
= 864 square inches
Since the trapezoid is made up of 3 triangles (with areas 1/2 base x height), we need to subtract the area of these triangles from the area of the rectangle.
Area of trapezoid = Area of rectangle - 3 x Area of triangle
= 864 - 3 * (1/2 * 6 * 18)
= 864 - 162
= 702 square inches
Therefore, the area of the trapezoid-shaped tabletop is 702 square inches.