Prove the area of a right triangle is equal to half the base*height

Prove that the area of a triangle is equal to 1/2*base*height.

The essence of this proof is to show that any right triangle can be made into a rectangle of the same base and height.

Consider the following two triangles:


Both these triangles can be made into rectangles with the same base and height as shown below:


The area of a rectangle is length times width, or in this case base times height.
The hypotenuse of the triangle cuts the rectangle directly in half, and thus the area of a triangle is 1/2 of a rectangle, or 1/2 base times height.