(a) This is similar to the example and the first problem. However, instead of measuring the distance from the point of the triangle to the slice, y measures the distance from the base of the triangle to the slice.
We will call the length of a slice x. When we use similar triangles to find x, we have to make sure to write 8 – y for the height of the smaller triangle. We know that
The area of the slice at height y is
Since y ranges from 0 (at the bottom of the triangle) to 8 (at the top of the triangle) the area of the triangle is