Chapter 1, Equations and Inequalities - 1.4 Rewrite Formuilas and Equations - 1.4 Exercises - Skill Practice - Page 31: 32

$$A=\frac{C^2}{4\pi}$$

The area of a circle is given by: $$A=\pi r^2(1)$$ From the formula of circumference ($C$), we can define $r$: $C=2\pi r$ $r=\frac{C}{2\pi}$ We simply substitute the value of $r$ in the first equation and get the following: $A=\pi (\frac{C}{2\pi})^2$ $= >$ $\pi \times \frac{C^2}{2^2\pi^2}$ $= >$ $\frac{C^2}{4\pi}$ $$A=\frac{C^2}{4\pi}$$