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
756 square inches
756 square inches
882 square inches
882 square inches
864 square inches
To find the area of the trapezoid-shaped tabletop, we can create a rectangle by extending the height line to the longer side to form a right triangle with the base of the trapezoid. This right triangle has a base of 36 + 6 = 42 and a height of 18.
Therefore, the area of this right triangle is (1/2) * base * height = (1/2) * 42 * 18 = 378 square inches.
Since the trapezoid is made up of the right triangle and the smaller trapezoid above it, we can add the area of the right triangle to the area of the larger trapezoid to find the total area of the tabletop.
The area of the larger trapezoid is calculated as 48 (longer side) + 36 (shorter side) * height (18) / 2 = 792 square inches.
Adding the area of the right triangle to the area of the trapezoid gives us a total of 378 + 792 = 1170 square inches.
Therefore, the area of the trapezoid-shaped tabletop is 1170 square inches.