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
A. 756 square inches
B. 648 square inches
C. 864 square inches
D. 882 square inches
To find the area of the trapezoid-shaped tabletop, we can create a rectangle by adding a triangle on the right side of the trapezoid such that the longer side of the trapezoid becomes the base of the rectangle and the height of the trapezoid becomes the height of the rectangle.
The longer base of the trapezoid is 48 and the shorter base is 36, so the length of the rectangle is 48. The height of the trapezoid (perpendicular height from the bottom left vertex to the longer side) is 18, which is also the height of the rectangle.
The area of a rectangle is length x width, so the area of the rectangle is 48 x 18 = 864 square inches.
Therefore, the area of the trapezoid-shaped tabletop is 864 square inches.
The correct answer is C. 864 square inches.