Equilateral Triangle Formula
Equilateral triangles have equal sides, as the name suggests. Every Equilateral Triangle Formula has the same internal angles, namely 60 degrees.
According to the length of their sides, triangles can be divided into three types:
- The angles and sides of a scalene triangle are unequal.
- Triangles with equal sides and angles are called equilateral triangles.
- Two sides and two angles of an isosceles triangle are equal.
What is an Equilateral Triangle?
An equilateral triangle’s area is defined as the region enclosed by its three sides. Square units are used to express it. An equilateral triangle’s area is usually measured in square meters, cubic meters, and square yards. On the Extramarks educational portal, there is a discussion of the area of the Equilateral Triangle Formula, the altitude of the Equilateral Triangle Formula, the perimeter of the equilateral triangle, and the semi-perimeter of an equilateral triangle.
Area of Equilateral Triangle
Equilateral triangles occupy equal amounts of space in a two-dimensional plane. An equilateral triangle is a triangle with equal sides and 60° internal angles. The area of an equilateral triangle can be calculated if one of its sides is known. The educators at Extramarks can help students to clear basics about the concept easily and effectively.
Area of the Equilateral Triangle Formula
The equilateral triangle area formula is used to calculate the area between the sides of an Equilateral Triangle Formula in a plane.
Calculating the area of a triangle with a known base and height is as follows:
Half of the base times the height equals the area
An equilateral triangle’s area can be calculated using the following formula:
Area = √3/4 × (side)2 square units
Perimeter of the Equilateral Triangle Formula
Triangles have a perimeter equal to the sum of the lengths of their three sides, whether they are equal or not.
Three sides of an equilateral triangle make up its perimeter.
The formula P= 3a is used to calculate the perimeter of an Equilateral Triangle Formula, where ‘a’ represents one of the sides. In an equilateral triangle, all three sides are equal, so a + a + a = 3a.
The height is calculated as √3a/ 2
A semi perimeter is equal to (a + a + a)/2 = 3a/2
Formulas and Calculations for an Equilateral Triangle:
- P = 3a, the perimeter of an Equilateral Triangle Formula
- The formula for semi-perimeter of an Equilateral Triangle: s = 3a/2
- Area of Equilateral Triangle Formula: K = (1/4) * √3 * a2
- The angles of an Equilateral Triangle are A = B = C = 60 degrees
- The sides of an Equilateral Triangle Formula are a, b, and c.
- Find the perimeter, semi perimeter, area, and altitude of a triangle given its side.
- a is known here; find P, s, K, h.
- h = (1/2) * √3 * a
- P equals 3a
- s = 3a/2
- K = (1/4) * √3 * a2
- Find the side, semi-perimeter, area, and altitude of the triangle based on the perimeter.
- h = (1/2) * √3 * a
- a = P/3
- s = 3a/2
- K = (1/4) * √3 * a2
- Find the side, perimeter, area, and altitude of a triangle given its semi-perimeter.
- Semi perimeter (s) is known; find a, P, K, and h.
- h = (1/2) * √3 * a
- a = 2s/3
- P = 3a
- K = (1/4) * √3 * a2
- Calculate the area, side, perimeter, semi-perimeter, and altitude of the triangle given its area.
- K is known; find a, s, h and P.
- a = √
- P = 3a
- s = 3a / 2
- h = (1/2) * √3 * a
- (4/√3)∗K
- (4/√3)∗K equals 2 * √
- K/√3
- K/√3
- Find the side, perimeter, semi-perimeter, and area based on the altitude/height
- P = 3a
- s = 3a/2
- a = (2/√3) * h
- K = (1/4) * √3 * a2
Solved Example
- Find the area of an Equilateral Triangle Formula with 12 inches on each side using the equilateral triangle area formula.
Solution:
Side = 12 in
Using the equilateral triangle area formula,
Area = √3/4 × (Side)2
= √3/4 × (12)2
= 36√3 in2
Answer: Area of an Equilateral Triangle Formula is 36√3 in2
- Find the perimeter and semi-perimeter of an Equilateral Triangle Formula with 12 units of side measurement.
Solution:
The perimeter = 3a
Semi-perimeter = 3a/ 2
Given, side a = 12 units
Equilateral triangles have the following perimeter:
3 × 12 = 36 units
An equilateral triangle’s semi-perimeter is equal to:
36/2 = 18 units.
- Imagine an Equilateral Triangle Formula with a side of 5 cm. In the given equilateral triangle, what will be its perimeter?
The perimeter of an Equilateral Triangle Formula can be calculated using the formula 3a.
Here, a = 5 cm
Therefore, the perimeter equals 3 × 5 cm, or 15 cm.