# GMAT Math : Calculating the area of an equilateral triangle

## Example Questions

### Example Question #1 : Equilateral Triangles

Three straight sticks are gathered of exactly equal length. They are placed end to end on the ground to form a triangle. If the area of the triangle they form is 1.732 square feet. What is the length in feet of each stick?

Explanation:

Let  be the length of a side of an equilateral triangle. Then the formula for the area of an equilateral triangle with side  is

So solving

we get .

Alternative Solution:

Without knowing this formula you can still use the Pythagorean Theorem to solve this. By drawing the height of the triangle, you split the triangle into 2 right triangles of equal size. The sides are the height,  and . Letting  stand for the unknown height, we solve

solving for  we get

The area for any triangle is the base times the height divided by 2. So

or .

### Example Question #1 : Calculating The Area Of An Equilateral Triangle

If an equilateral triangle has a side length of and a height of , what is the area of the given triangle?

Explanation:

To find the area of a traingle, we need the height and base lengths. Plug the given values into the following formula:

### Example Question #7 : Equilateral Triangles

Triangle  is an equilateral triangle with side length . What is the area of the triangle?

Explanation:

The area of an equilateral triangle is given by the following formula:

, where  is the length of a side.

Since we know the length of the side, we can simply plug it in the formula and we have  or , which is the final answer.

### Example Question #1 : Calculating The Area Of An Equilateral Triangle

is an equilateral triangle inscribed in a cirlce with radius . What is the area of the triangle ?

Explanation:

Since we are given a radius for the circle, we should be able to find the length of the height of the equilateral triangle, indeed, the center of the circle is  of the length of the height from any vertex.

Therefore, the height is  where  is the length of the height of the triangle. Therefore .

We can now plug in this value in the formula of the height of an equilateral triangle, where  is the length of the side of the triangle.

Therefore,  or .

Now we should plug in this value into the formula for the area of an equilateral triangle  where  is the value of the area of the equilateral triangle. Therefore , which is our final answer.

### Example Question #9 : Equilateral Triangles

A given equilateral triangle has a side length  and a height  . What is the area of the triangle?

Not enough information provided

Explanation:

For a given equilateral triangle with a side length  and a height , the area  is

. Plugging in the values provided:

### Example Question #10 : Equilateral Triangles

A given right triangle has a base length  and a height  . What is the area of the triangle?

Not enough information to solve

Explanation:

For a given right triangle with a side length  and a height , the area  is

. Plugging in the values provided:

### Example Question #1 : Calculating The Area Of An Equilateral Triangle

A given right triangle has a base of length  and a height  . What is the area of the triangle?

Not enough information to solve