When does the derivative of area equal perimeter?

Many polygons have an incircle with radius a. In many cases, the perimeter P and area A will be functions of a. Regular polygons (and circles) have dAda=P. A method using proportionality and simple differentiation is used to extend this result to all tangential polygons. The result is not true for rectangles. No integration or geometry is required, unlike some proofs for regular polygons. Further, the method used easily generates dVda=S for all five Platonic solids. Additionally, several results on tangential polygons and tangential quadrilaterals are given.