The formula can be formally proved using calculus. By similarity, the "linear" dimensions of a cross-section parallel to the base increase linearly from the apex to the base. The scaling factor (proportionality factor) is formula_2, or formula_3, where "h" is the height and "y" is the perpendicular distance from the plane of the base to the cross-section. Since the area of any cross-section is proportional to the square of the shape's scaling factor, the area of a cross-section at height "y" is formula_4, or since both "b" and "h" are constants, formula_5. The volume is given by the integral