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
648 square inches
864 square inches
882 square inches
To find the area of the trapezoid-shaped tabletop, we first need to find the area of the rectangle that can be composed from the trapezoid. This rectangle would have a base length of 36 (the shorter base of the trapezoid) and a height of 18 (the perpendicular height from the bottom left vertex to the longer side).
Area of the rectangle = base x height
Area of the rectangle = 36 x 18
Area of the rectangle = 648 square inches
Since the trapezoid can be split into a rectangle and a smaller trapezoid, the area of the trapezoid is equal to the sum of the areas of the rectangle and the smaller trapezoid.
The area of the trapezoid = area of rectangle + area of smaller trapezoid
Area of the trapezoid = 648 + 108 (calculated separately)
Area of the trapezoid = 756 square inches
Therefore, the area of the tabletop is 756 square inches.