The base times the height, as you may know, is equal to the area of a rectangle. Once you half that, it becomes the area of a triangle. Let me explain more:
(Picture of right triangle)
As you can see, this triangle is a right triangle. I am only choosing this because it is the easiest to explain. Once you take another right triangle with exactly the same measurements, you can see in the picture below how it becomes a rectangle.
Because of this, the area of a triangle is equal to the area of the rectangle divided by two, or the base times the height divided by two, or, 1/2*B*H