What is the area of an equilateral triangle with an apothem 2cm long and a side 6.9 cm long?

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Answer 1 · 2015-12-14T23:43:07

$20.7 {cm}^{2}$ $20.7 "cm"^2$

Because your triangle is equilateral, we can use the formula for the area of an regular polygon:

$A = \frac{1}{2} a P$ $A = 1/2aP$

where $a$ $a$ is the apothem and $P$ $P$ is the perimeter.

The number of sides in a triangle is 3, so $P = 3 \cdot 6.9 cm = 20.7 cm$ $P = 3 * 6.9 "cm" = 20.7 "cm"$ .

We've already been given $a$ $a$ , so now we can plug in our values:

$A = \frac{1}{2} a P = \frac{1}{2} (2) (20.7) = 20.7 {cm}^{2}$ $A = 1/2aP = 1/2(2)(20.7) = 20.7 "cm"^2$