Use Area to Solve Problems Quick Check
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Question
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
882 square inches
882 square inches
648 square inches
648 square inches
864 square inches
To find the area of the trapezoid-shaped tabletop, we first need to find the area of the rectangle created by the shorter base and the height of the trapezoid.
The height of the trapezoid is 18 inches, and the shorter base is 36 inches. So, the area of the rectangle is 36 inches * 18 inches = 648 square inches.
Since the trapezoid is made up of a rectangle and a triangle, we also need to find the area of the triangle. The base of the triangle is the difference between the longer and shorter bases, which is 48 inches - 36 inches = 12 inches. The height of the triangle is given as 6 inches.
So, the area of the triangle is 0.5 * base * height = 0.5 * 12 inches * 6 inches = 36 square inches.
Therefore, the total area of the trapezoid-shaped tabletop is the sum of the area of the rectangle and the area of the triangle, which is 648 square inches + 36 square inches = 684 square inches.
Therefore, the correct answer is not provided in the answer choices. The closest answer is 648 square inches.