Area of a parallelogram and of a triangle

Any side of a parallelogram can be taken as the base; the distance from it to the opposite side is then the altitude, which sometimes falls on the extension of a side. Theorem: the area of a parallelogram equals the product of its base and altitude: S = a · h. Proof: moving a triangle from one end of the parallelogram to the other gives a rectangle with base a and height h; the two figures are equidecomposable, and the rectangle has area ah. Consequence: parallelograms with the same base and equal altitudes have equal area. The area can be computed with either side as the base: S = a · ha = b · hb.