Answer
A = $\pi r^{2}$
We know d = 2r
r = $\frac{d}{2}$
A = $\pi (\frac{d}{2})^{2}$
= $\pi \frac{d^{2}}{4}$
Work Step by Step
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 = $\pi \frac{d^{2}}{4}$
