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 find the area of the rectangle and then subtract the area of the two right triangles on either end.
The rectangle's height is 18 inches (perpendicular height) and its length is the sum of the shorter base and the length between the top left vertex and the height intersection, which is 36 + 6 = 42 inches.
So, the area of the rectangle is 18 * 42 = 756 square inches.
Next, we find the areas of the two right triangles:
- The first right triangle has a base of 36 and a height of 18, so its area is (1/2) * 36 * 18 = 324 square inches.
- The second right triangle has a base of 6 and a height of 21, so its area is (1/2) * 6 * 21 = 63 square inches.
Total area of the two right triangles = 324 + 63 = 387 square inches.
Therefore, the area of the trapezoid-shaped tabletop is the area of the rectangle minus the area of the two right triangles:
756 - 387 = 369 square inches.