To find the area of the trapezoid, we can create a rectangle by extending the shorter base to make it the longer base of the rectangle. The height of the rectangle would be the same as the height of the trapezoid, which is 18 inches.
The dimensions of the rectangle would be 48 inches by 36 inches. Therefore, the area of the rectangle would be:
Area = length x width
Area = 48 inches x 36 inches
Area = 1728 square inches
Since the trapezoid represents a portion of the rectangle, we can find the area of the trapezoid by subtracting the area of the smaller triangle at the top. To find the area of the smaller triangle, we can use the formula for the area of a triangle: 1/2 x base x height.
The base of the smaller triangle would be 6 inches and the height would be 18 inches. Therefore, the area of the smaller triangle would be:
Area = 1/2 x 6 inches x 18 inches
Area = 54 square inches
Now, we can find the area of the trapezoid by subtracting the area of the smaller triangle from the area of the rectangle:
Area of trapezoid = Area of rectangle - Area of smaller triangle
Area of trapezoid = 1728 square inches - 54 square inches
Area of trapezoid = 1674 square inches
Therefore, the area of the trapezoid-shaped tabletop is 1674 square inches.
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 answer