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# Express the area of an equilateral triangle as a function of its perimeter?

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7
Dec 1, 2015

The area of an equilateral triangle with side $a$ is

$A = \frac{\sqrt{3}}{4} \cdot {a}^{2}$

The perimeter P is $P = 3 \cdot a$ or $a = \frac{P}{3}$ hence

$A = \frac{\sqrt{3}}{4} \cdot {\left(\frac{P}{3}\right)}^{2}$

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