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
882 square inches
882 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 use the formula for the area of a trapezoid:
Area = (1/2) * (a + b) * h
Where a and b are the lengths of the two parallel sides (36 and 48 in this case), and h is the perpendicular height (18 in this case).
First, compose a rectangle using the trapezoid by adding a triangle to the smaller base. The base of the triangle would be 48 - 36 = 12, and the height would be 18. Therefore, the area of the rectangle would be:
Area = 48 * 18 = 864 square inches
Now, we need to subtract the area of the triangle from the rectangle to get the area of the trapezoid:
Triangle Area = (1/2) * base * height
Triangle Area = (1/2) * 12 * 18
Triangle Area = 108 square inches
Trapezoid Area = Rectangle Area - Triangle Area
Trapezoid Area = 864 - 108
Trapezoid Area = 756 square inches
Therefore, the area of the trapezoid-shaped tabletop is 756 square inches.