(a) The variable h measures the distance from the right endpoint of the triangle to the slice. When h = 0 the slice is at the right tip of the triangle, and when h = 10 the slice is all the way on the left.
We will call the height of a slice y. We have similar triangles again. This means
The area of the slice at distance h from the right tip of the triangle is
The limits of integration are the values that make sense for h, which are 0 to 10, so the area of the triangle is