the radius of the excircle on the hypotenuse equals the semiperimeter. The semiperimeter is the sum of the inradius and twice the circumradius. The area of the right triangle is where are the legs. For quadrilaterals The formula for the semiperimeter of a quadrilateral with side lengths is One of the triangle area formulas involving the semiperimeter also applies to tangential quadrilaterals, which have an incircle and in which (according to Pitot's theorem) pairs of opposite sides have lengths summing to the semiperimeter—namely, the area is the product of the inradius and the semiperimeter: The simplest form of Brahmagupta's formula for the area of a cyclic quadrilateral has a form similar to that of Heron's formula for the triangle area: Bretschneider's formula generalizes this to all convex quadrilaterals: in which and are two opposite angles. The four sides of a bicentric quadrilateral are the four solutions of a quartic equation parametrized by the semiperimeter, the inradius, and the circumradius. Regular polygons The area of a convex regular polygon is the product of its semiperimeter and its apothem. See also Semidiameter References External links Triangle geometry