In the mathematical theory of conformal mappings, the area theorem gives an inequality satisfied by the power series coefficients of specific conformal mappings. The theorem is called by that name, not because of its implications, but rather proof uses the notion of area. Area Theorem: The ratio of areas of two similar triangles is equal to the squares of the ratio of their corresponding sides. If two triangles are similar, then the ratio of the area of both triangles is proportional to the square of the ratio of their corresponding sides. It proves that the ratio of the area of two similar triangles is proportional to the squares of the corresponding sides of both the triangles.