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
882 square inches
882 square inches
648 square inches
648 square inches
756 square inches
756 square inches
864 square inches
To find the area of the trapezoid-shaped tabletop, we can create a rectangle by extending the shorter base of length 36 with a length of 48 to form a rectangle. This rectangle can be split into two congruent right triangles and the trapezoid itself.
The area of the rectangle is 36 x (36 + 48) = 36 x 84 = 3024 square inches.
The area of one of the right triangles is (1/2) x 21 x 18 = 189 square inches. Since the trapezoid is made of two congruent right triangles, the combined area of both right triangles is 2 x 189 = 378 square inches.
Subtracting the area of the two right triangles from the area of the rectangle gives us the area of the trapezoid:
3024 - 378 = 2646 square inches
Therefore, the area of the trapezoid-shaped tabletop is 2646 square inches.
wrong
My apologies for the error. Let's recalculate.
The area of a trapezoid can be given by the formula: (1/2) x (sum of bases) x height
In this case, the sum of bases is (36 + 48) = 84 and the height is 18.
Therefore, the area of the trapezoid-shaped tabletop is:
(1/2) x 84 x 18 = 756 square inches.
Thus, the area of the tabletop is 756 square inches.