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?
To find the area of the trapezoid-shaped tabletop, we can first calculate the area of the rectangle inside the trapezoid.
The rectangle has a base 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). The area of the rectangle is base x height = 36 x 18 = 648 square inches.
Next, we need to calculate the area of the trapezoid itself. Since the trapezoid can be divided into a rectangle and two right triangles, we can find the total area by adding the areas of these three shapes.
The two right triangles each have a base of 6 (the length between the top left vertex of the longer side and where the height meets the longer side) and a height of 18 (the perpendicular height). The area of one right triangle is 1/2 x base x height = 1/2 x 6 x 18 = 54 square inches. Since there are two right triangles, the total area of both triangles is 2 x 54 = 108 square inches.
Finally, the area of the trapezoid is the sum of the area of the rectangle and the total area of the two right triangles: 648 (rectangle) + 108 (right triangles) = 756 square inches.
Therefore, the area of the tabletop is 756 square inches.