Use the integral method to show that the area of the triangle can be obtained by multiplying 1/2 of the base?

Question

Use the integral method to show that the area of the triangle can be obtained by multiplying 1/2 of the base by the height.

Answer 1

Let y = mx
integral 0 to x (mx) =m x^2/2 evaluated from 0 to x
= mx^2/2 - 0 =mx^2/2
Since m= y/x, A = xy/2 = area under the line y=mx

Answer 2

Create the function f(x) as follows:
one base vertex is the origin of coordinates, and the base is the x-axis.

Suppose the coordinate of the other base vertex is x = d, and suppose the height h to the third vertex occurs at x = d - c

Area = Integral{limits 0, d-c}[h/(d - c)]x dx
+ Integral{limits d-c, d}[- (h/c)][x - d] dx