Question

Find the area of the trapezoid by decomposing it into other shapes.
112 u^2
420 u^2
98 u^2
56 u^2

Answer 1

To find the area of the trapezoid, we can decompose it into a rectangle and two triangles.

First, let's label the trapezoid. We have the top base with a length of 112u^2, the bottom base with a length of 420u^2, the height of the trapezoid is 98u^2, and the slant height is 56u^2.

To decompose the trapezoid, we will create a rectangle and two triangles. The rectangle will have a length equal to the top base and bottom base, and a height equal to the height of the trapezoid. The two triangles will be formed by the slant height of the trapezoid and the height of the trapezoid.

The area of the rectangle is length times width, so the area of the rectangle is 112u^2 * 98u^2 = 10976u^4.

The area of each triangle is 1/2 * base * height. In this case, the base is the slant height and the height is the height of the trapezoid. So the area of each triangle is 1/2 * 56u^2 * 98u^2 = 2744u^4.

To find the total area of the trapezoid, we add the area of the rectangle and the area of both triangles:
Total area = area of rectangle + 2 * area of triangle
Total area = 10976u^4 + 2 * 2744u^4
Total area = 10976u^4 + 5488u^4
Total area = 16464u^4

Therefore, the area of the trapezoid is 16464u^4.