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
756 square inches
756 square inches
648 square inches
648 square inches
864 square inches
To find the area of the trapezoid-shaped tabletop, we need to first find the height of the trapezoid.
The height of the trapezoid can be found by using the Pythagorean theorem on the small triangle formed by the height, the given length of 6, and the leg of length 21. This small triangle is a right triangle.
Using the Pythagorean theorem:
(21)^2 = 6^2 + height^2
441 = 36 + height^2
Height = √(405)
Height = 9√5
Now that we have the height, we can find the area of the trapezoid using the formula:
Area = (1/2)(sum of bases)(height)
Area = (1/2)(36+48)(9√5)
Area = (1/2)(84)(9√5)
Area = 42 * 9√5 = 378√5 ≈ 847.23 square inches
So, the area of the trapezoid-shaped tabletop is approximately 847.23 square inches.