Equilateral Triangle Formula

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What is an Equilateral Triangle?

  • As the name suggests, ‘equi’ means equal, and an equilateral triangle is the one in which all sides are equal.

  • The internal angles of any given equilateral triangle are of the same measure, that is, equal to 60 degrees.

What is the Area of Equilateral Triangle Formula?

The area of an equilateral triangle is the amount of space that it occupies in a 2-dimensional plane. To recall, an equilateral triangle can be defined as a triangle in which all the sides are equal and the measure of all the internal angles is 60°. So, an equilateral triangle’s area can be calculated if the length of any one side of the triangle is known.

The Perimeter of Equilateral Triangle Formula

The perimeter of a triangle is equal to the sum of the length of its three sides, whether they are equal or not.

Here is a list of the area of the equilateral triangle formula, the altitude of the equilateral triangle formula, the perimeter of the equilateral triangle formula, and the semi-perimeter of an equilateral triangle.

Formulas and Calculations for an Equilateral Triangle:

  • Perimeter of Equilateral Triangle: P = 3a

  • Semiperimeter of Equilateral Triangle Formula: s = 3a/2

  • Area of Equilateral Triangle Formula: K = (1/4) * √3 * a2

  • The altitude of Equilateral Triangle Formula: h = (1/2) * √3 * a

  • Angles of Equilateral Triangle: A = B = C = 60 degrees

  • Sides of Equilateral Triangle: a equals b equals c.

1. Given the side of the triangle find the perimeter, semiperimeter, area, and altitude.

  • a is known here; find P, s, K, h.

  • P equals 3a

  • s = 3a/2

  • K = (1/4) * √3 * a2

  • h = (1/2) * √3 * a

2. Given the perimeter of triangle find the side, semiperimeter, area, altitude.

  • Perimeter(P) is known; find a, s, K, and h.

  • a = P/3

  • s = 3a/2

  • K = (1/4) * √3 * a2

  • h = (1/2) * √3 * a

3. Given the semi perimeter of a triangle find the side, perimeter, area, and altitude.

  • Semiperimeter (s) is known; find a, P, K, and h.

  • a = 2s/3

  • P = 3a

  • K = (1/4) * √3 * a2

  • h = (1/2) * √3 * a

4. Given the area of the triangle find the side, perimeter, semiperimeter, and altitude.

  • K is known; find a, P, s and h.

  • a = √[(4 / √3) * K] equals 2 * √[K/√3]

  • P = 3a

  • s = 3a / 2

  • h = (1/2) * √3 * a

5. Given the altitude/height find the side, perimeter, semiperimeter, and area

  • Altitude (h) is known; find a, P, s, and K.

  • a = (2/√3) * h

  • P = 3a

  • s = 3a/2

  • K = (1/4) * √3 * a2

Solved Examples

Question 1) Suppose you have an equilateral triangle with a side of 5 cm. What will be the perimeter of the given equilateral triangle?

Solution) We know that the formula of the perimeter of an equilateral triangle is 3a.

Here, a = 5 cm

Therefore, Perimeter = 3 * 5 cm = 15 cm.

FAQ (Frequently Asked Questions)

Question 1. What is the Equilateral Triangle?

Answer: An equilateral triangle is a triangle with all three sides of equal length, corresponding to what could also be known as a "regular" triangle. An equilateral triangle is known as a special case of an isosceles triangle having not just two, but all three sides equal. An equilateral triangle also has three equal.

Question 2. Is an Equilateral Triangle Unique?

Answer: A triangle has all three of its sides equal in length. An equilateral triangle is one in which all 3 sides are congruent (same length). Because it has the property that all three interior angles are equal.

Question 3. What is the Height of the Triangle or What is the Altitude of a Triangle?

Answer: Every side of the triangle can be a base, and from every vertex, you can draw the line perpendicular to a line containing the base - that's the height of the triangle. Every triangle has three heights, which are also known as altitudes.