Algebra 2 (1st Edition)

Published by McDougal Littell
ISBN 10: 0618595414
ISBN 13: 978-0-61859-541-9

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

Answer

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

Work Step by Step

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: $A=\pi (\frac{C}{2\pi})^2$ $= >$ $\pi \times \frac{C^2}{2^2\pi^2}$ $= >$ $\frac{C^2}{4\pi}$ $$A=\frac{C^2}{4\pi}$$
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