# Equilateral Triangle Formulas

An equilateral triangle is a triangle for which the measure of all sides is equal and all its angles measure 60º. Equilateral triangle formulas are used to calculate the perimeter, area and height,of an equilateral triangle.

## What Are Equilateral Triangle Formulas?

An equilateral triangle is the one in which all sides of the triangle are equal and have equal angles measures. Equilateral triangle formulas are used to calculate the area, altitude, perimeter, and semi-perimeter of an equilateral triangle.

### Equilateral Triangle Formulas

Equilateral triangle formulas are used to calculate different parameters of an equilateral triangle.

- Formula to calculate area of an equilateral triangle is given as:

Area of an equilateral triangle, A = (√3/4)a^{2}, where a is the side of the equilateral triangle. - Formula to calculate perimeter of an equilateral triangle is given as:

Perimeter of an equilateral triangle, P = 3a, where a is the side of the equilateral triangle. - Formula to calculate semi-perimeter of an equilateral triangle is given as:

Semi perimeter of an equilateral triangle = 3a/2, where a is the side of the equilateral triangle. - Formula to calculate height of an equilateral triangle is given as:

Height of an equilateral triangle, h = (√3/2)a, where a is the side of the equilateral triangle.

## Examples Using Equilateral Triangle Formulas

**Example 1:** If the perimeter of an equilateral triangle is 99 units, what would be the length of each side of an equilateral triangle?

**Solution:**

To find: Length of each side of an equilateral triangle.

Given: Perimeter of an equilateral triangle = 99 Units

Using equilateral triangle formulas for perimeter,

The perimeter of an equilateral triangle = 3a

99 = 3a

a = 99/3

a = 33 Units

**Answer: The length of each side of the given equilateral triangle is 33 Units.**

**Example 2: **If each side of an equilateral triangular park measures 200 m, calculate its area.

**Solution: **

To find: Area of an equilateral triangular park.

Length of each side of the park = 200m

Using equilateral triangle formulas for the area,

Area of an Equilateral Triangle = (√3/4)a^{2}

=√3/4(200)^{2}

= 17,320.508 m^{2}

**Answer: The area of an equilateral triangular park is 17,320.508 m ^{2}.**

**Example 3: **Calculate the area, altitude, perimeter, and semi-perimeter of an equilateral triangle whose side is 10 units.

**Solution:**

Side of an equilateral triangle = a = 10 units

Area of an equilateral triangle

= √3/4 a^{2}

= √3/4 × 10^{2} unit^{2}

= √3/4 × 100 unit^{2}

= 43.30 unit^{2}

Altitude of an equilateral triangle

= √3/2 a

= √3/2 × 10 units

= 8.66 units

Perimeter of an equilateral triangle

= 3a

= 3 × 10 units

= 30 units

Semi-Perimeter of an equilateral triangle

= 3a/2

= (3×10)/2 units

= 15 units

**Answer: Area = 43.3 sq units, Altitude= 8.66 units , Perimeter = 30 units, Semi-perimeter = 15 units**

## FAQs on Equilateral Triangle Formulas

### What Is Equilateral Triangle Formula in Geometry?

In geometry, equilateral triangle formulas are formulas that are used to calculate the area, altitude, perimeter, and semi-perimeter of an equilateral triangle using the measure of its side.

### How To Use Equilateral Triangle Formula?

We can use the equilateral triangle formulas as follows:

- Step 1: Check for the parameter to be derived or calculated.
- Step 2: Identify the side of the equilateral triangle and put the value in the required formula - area, perimeter, altitude, or semi-perimeter.

In case, area, perimeter, altitude, or semi-perimeter of the equilateral triangle are given, you can find the measure of the side of the triangle by equating the given values to the respective equilateral triangle formula.

### What Is 'a' in Equilateral Triangle Formula?

In an equilateral triangle formula, be it area, perimeter, altitude, or semi-perimeter, 'a' refers to the measure of the side of the equilateral triangle.

- Area of an equilateral triangle, A = (√3/4)a
^{2} - Perimeter of an equilateral triangle, P = 3a
- Semi perimeter of an equilateral triangle = 3a/2
- Height of an equilateral triangle, h = (√3/2)a

### How To Find Side of Triangle Using Equilateral Triangle Formula?

An equilateral triangle has three sides of equal measure. Also, all equilateral triangle formulas are dependent on the side of the equilateral triangle, say a. Thus,

- If area is known, put the given value equal to (√3/4)a
^{2}, and by simplifying it calculate a. - If perimeter is known, put the given value equal to 3a, and solving it further gives the side a.
- If altitude is known, put the given value equal to (√3/2)a and find the value of a.

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