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
648 square inches
648 square inches
864 square inches
864 square inches
882 square inches
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. The width of the rectangle is 36 (length of the shorter base) and the height of the rectangle is 18 (perpendicular height from the bottom left vertex to the longer side).
Area of the rectangle = 36 * 18 = 648 square inches
Now, we need to find the area of the trapezoid by subtracting the area of the two right triangles from the rectangle.
Area of trapezoid = Area of rectangle - 2*(1/2 * base of right triangle * height of right triangle)
Area of trapezoid = 648 - 2*(1/2 * 6 * 18) = 648 - 2*(3 * 18) = 648 - 108 = 540 square inches
Therefore, the area of the trapezoid-shaped tabletop is 540 square inches.