## Elementary Geometry for College Students (6th Edition)

A = $\pi r^{2}$ We know d = 2r r = $\frac{d}{2}$ A = $\pi (\frac{d}{2})^{2}$ = $\pi \frac{d^{2}}{4}$
Given length of diameter of the circle = d We need to explain why A(circle) = $\frac{\pi}{4} d^{2}$ The area A of a circle whose radius has length r is given by A = $\pi r^{2}$ We know d = 2r r = $\frac{d}{2}$ By putting r = $\frac{d}{2}$ in area formula A = $\pi (\frac{d}{2})^{2}$ = $\pi \frac{d^{2}}{4}$ Therefore A = $\pi \frac{d^{2}}{4}$