# Find the area of an equilateral triangle with apothem 7 cm? Round to the nearest whole number.

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help me.

help me.

##### 1 Answer

#### Answer:

I got

#### Explanation:

The apothem of the triangle will also be the triangle's height.

Let's work out the height of an equilateral triangle in terms of its sides.

Say we have an equilateral triangle of side

Its height will be the perpendicular bisector of another side, let's call it

As you can see here, we split the triangle into

Now, let's work out the height

We can use Pythagoras's theorem to work out the height,

We got:

So, the height of an equilateral triangle with sides

Now, we can put this formula back into our original problem.

We have the apothem or the triangle's height as

So, the triangle's side will be

The area of a triangle is given by

Plugging in our values, we get