# GMAT Math : Equilateral Triangles

## Example Questions

### Example Question #7 : 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

Explanation:

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

. Plugging in the values provided:

### Example Question #11 : Equilateral Triangles

If the area of an equilateral is , given a base of , what is the height of the triangle?

Explanation:

We derive the height formula from the area of the triangle formula:

### Example Question #12 : Equilateral Triangles

What is the height of an equilateral triangle with sidelength 20?

Explanation:

The area of an equilateral triangle with sidelength  is

Using this area for  and 20 for  in the general triangle formula, we can obtain :

### Example Question #13 : Equilateral Triangles

An equilateral triangle has a side length of . What is the height of the triangle?

Explanation:

The height of an upright equilateral triangle is the perpendicular distance from the center of its base to its top. We can imagine that this line cuts the equilateral triangle into two congruent right triangles whose height is half the length of the original base and whose hypotenuse is the original side length. In these two congruent triangles, their base, which is the height of the equilateral triangle, is the only unknown side length, so we can use the Pythagorean theorem to solve for it:

### Example Question #14 : Equilateral Triangles

is an equilateral triangle, with a side length of . What is the height of the triangle?

Explanation:

We know the length of the side, therefore we can use the formula for the height in an equilateral triangle:

, where  is the length of a side and  the length of the height.

Therefore, the final answer is .

### Example Question #15 : Equilateral Triangles

Given that an equilateral triangle has side lengths equal to , determine it's height in simplest form.

Explanation:

To solve, we must use pythagorean's theorem given that we know the hypotenuse is  and one side length is  . Therefore:

### Example Question #16 : Equilateral Triangles

The area of an equilateral triangle  is . What is the perimeter of ?

Explanation:

The area is given, which will allow us to calculate the side of the triangle and hence we can also find the perimeter.

The area for an equilateral triangle is given by the formula

, where  is the length of the side of the triangle.

Therefore, , where  is the area.

Thus , and the perimeter of an equilateral triangle is three times the side, hence, the final answer is .

### Example Question #17 : Equilateral Triangles

A given equilateral triangle has a side length of . What is the perimeter of the triangle?

Not enough information provided.

Explanation:

An equilateral triangle with a side length  has a perimeter .

Given:

### Example Question #18 : Equilateral Triangles

A given equilateral triangle has a side length of . What is the perimeter of the triangle?

Explanation:

An equilateral triangle with a side length  has a perimeter .

Given:

### Example Question #19 : Equilateral Triangles

A given equilateral triangle has a side length of . What is the perimeter of the triangle?