# How do you find the area of an equilateral triangle with a 3 inch apothem?

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**Apothem** is the distance from the center of a regular polygon perpendicular to one of its side.

Refer to this figure:

In order to find the area of the triangle, we use the formula for **regular polygon**

Where:

This problem requires knowledge in trigonometry since the only given is the apothem.

We now know that in order to solve for the area, we need to have both the apothem and the measurement of sides.

Since, this is an equilateral triangle, we just need to find one side and to find its perimeter, we just multiply it by 3.

Using this figure we solve for the side:

We know that each angle of the triangle is **NOTE that this is only true for regular figures**

Now, take a closer look. Since we have formed a right triangle inside, we can use **trigonometric functions** to solve for **half of the side**.

Using **tangent function**:

**Now we have the side, we can now compute for the perimeter:**

**Then solving for area:**

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the apothem is the same as the height of the triangle.

there is a formula on equilateral triangles (it can on only be used if the triangle is equilateral). the formula is:

like this:

now that you have the measure of the triangles' sides you can find the area of the triangle:

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