The perimeter of an equilateral triangle is 24. What is the area?

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Answer 1 · 2016-04-27T16:48:06

The area $= 16 \sqrt{3} c m^{2}$ $= color(green)(16sqrt3 cm^2$

The perimeter of an equilateral triangle $(3 a)$ $(3a)$ is $= 24 c m$ $=24 cm$ (assuming units to be in cm)

Let us denote the side of the equilateral triangle as $a$ $a$

$3 a = 24$ $3a = 24$

$a = \frac{24}{3}$ $a = 24/3$

$a = 8 c m$ $color(green)(a = 8cm$

The formula for area of equilateral triangle is :
$\frac{\sqrt{3}}{4} (a^{2})$ $color(blue)(sqrt3/4 (a^2)$

$= \frac{\sqrt{3}}{4} (8^{2})$ $= sqrt3/4 (8^2)$

$= \frac{\sqrt{3}}{4} \cdot 64$ $= sqrt3/4 * 64$

$= 16 \sqrt{3} c m^{2}$ $= color(green)(16sqrt3 cm^2$