Equilateral Triangle Formula

What is an Equilateral Triangle?

An equilateral triangle is one in which all sides are equal, as the name implies. Any equilateral triangle has the same interior angles, which are all 60 degrees.

Triangles are divided into three types based on their side lengths: 

• Scalene triangle: The scalene triangle's sides and angles are not equal.
• Isosceles triangle: A triangle with two equal sides and two equal angles is called an isosceles triangle.
• Equilateral triangle: The equilateral triangle has equal sides and angles.

How to find Equilateral Triangle Area 

The area of an equilateral triangle is defined as the area contained by the three sides of the triangle. It's calculated in square units. The area of an equilateral triangle is commonly expressed in in², m², cm², and yd².

The area of an equilateral triangle, the height of an equilateral triangle, the perimeter of an equilateral triangle, and the semi-perimeter of an equilateral triangle are all addressed here.

An equilateral triangle's area is the amount of space it takes up in a two-dimensional plane. To refresh your memory, an equilateral triangle is a triangle with all sides equal and all internal angles measuring 60 degrees. If the length of any one of the triangle's sides is known, the area of the triangle can be computed. For more Maths formulas click on the main page. 

The equilateral triangle area formula is used to calculate the area occupied between the sides of an equilateral triangle in a plane.

1. The area of a triangle with a known base and height is calculated using the following formula:
2. Area = 1/2 × base × height
3. The area of an equilateral triangle can be calculated using the formula below:
4. Area = √3/4 × (side)² square units
5. Formulas and Calculations for an Equilateral Triangle:
6. Perimeter of Equilateral Triangle: P = 3a
7. Semiperimeter of Equilateral Triangle Formula: s = 3a/2
8. Area of Equilateral Triangle Formula: K = (1/4) * √3 * a²
9. The altitude of Equilateral Triangle Formula: h = (1/2) * √3 * a
10. Angles of Equilateral Triangle: A = B = C = 60 degrees
11. Sides of Equilateral Triangle: a equals b equals c.

Solved Example of Equilateral Triangle 

Example-1

The measure of one angle of an equilateral triangle is

(a)15°.

(b)30°.

(c)45°.

(d)60°.

Ans : (d). 

Explanation:

Sketch a triangle to help you plan your solution.

In your sketch, mark congruent sides alike.

Since all sides of the triangle are congruent, according to the fact above.

Let x represent the measure of one of the three congruent angles.

Then each angle has measured x, so

 x + x + x = 180°

 3x = 180°

x = 60°.

Each angle of an equilateral triangle has measured 60°.

Example-2

ABC is an equilateral triangle of side 2a, then the length of its altitude is 

(a)a cm.

(b)a√2 cm.

(c)a√3 cm.

(d)√3 cm.

Ans : (c).

Explanation:

Let AD be the altitude of the triangle.

Therefore, from the given figure, we have

AD2 = AC2 + DC2

 AD2 = (2a)2 - a2

 = 3a2.

Or AD = a√3 cm.

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