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 $= color(green)(16sqrt3 cm^2$

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

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

$3a = 24$

$a = 24/3$

$color(green)(a = 8cm$

The formula for area of equilateral triangle is :
$color(blue)(sqrt3/4 (a^2)$

$= sqrt3/4 (8^2)$

$= sqrt3/4 * 64$

$= color(green)(16sqrt3 cm^2$