# GMAT Math : Calculating the height of an equilateral triangle

## Example Questions

### Example Question #12 : Equilateral Triangles

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

Possible Answers:

Correct answer:

Explanation:

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

### Example Question #61 : Triangles

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

Possible Answers:

Correct answer:

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 #14 : Equilateral Triangles

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

Possible Answers:

Correct answer:

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 #15 : Equilateral Triangles

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

Possible Answers:

Correct answer:

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 #16 : Equilateral Triangles

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

Possible Answers:

Correct answer:

Explanation:

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