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
864 square inches
864 square inches
756 square inches
756 square inches
882 square inches
882 square inches
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To find the area of the trapezoid-shaped tabletop, we need to first find the area of the rectangle that can be composed within the trapezoid. The rectangle would have a base of 36 inches (shorter base of the trapezoid) and a height of 18 inches (perpendicular height from the bottom left vertex to the longer side).
Therefore, the area of the rectangle would be:
Area = base x height
Area = 36 in x 18 in
Area = 648 square inches
Since the trapezoid consists of the rectangle and two additional triangles on top, the area of the trapezoid would be the area of the rectangle plus the sum of the areas of the two triangles.
The area of each triangle would be:
1/2 x base x height
1/2 x 6 in x 21 in = 63 square inches (for each triangle)
Since there are two triangles, the total area of both triangles would be:
63 in + 63 in = 126 square inches
Adding this to the area of the rectangle, we get:
648 square inches + 126 square inches = 774 square inches
Therefore, the area of the trapezoid-shaped tabletop is 774 square inches.