Centre of Mass of Equilateral Triangle

In geometry, the equilateral triangle is a triangle in which all the three sides are equal. All the internal angles of the equilateral triangle are also equal. The angles are equal to 60⁰.

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How to Find Centre of Mass of Equilateral Triangle

The centre of mass can be calculated by following these steps

Step 1: Find the midpoint of all the three sides of the triangle.

Step 2: Draw a perpendicular from midpoint to the opposite vertex. This perpendicular line is called the median.

Step 3: These three medians meet at a point. This point of intersection of the medians is the centre of mass of the equilateral triangle.

The centre of mass of the equilateral triangle is at a distance of H/3 from the centre of the base of the triangle. H is the height of the triangle. The centroid or the centre of mass divides the median in 2:1 ratio.

Calculation of Distance of the Centre of Mass from the Vertex

Let a be the length of the sides. The internal angle of the equilateral triangle is 60⁰.

Using Pythagoras theorem,

Sin 60⁰ = AD/a

AD = (a√3)/2

Median of the equilateral triangle divides the median by the ratio 2:1

Therefore, OD = (a√3)/6

In triangle OBD

Sin 30⁰ = OD/OB

Sin 30⁰ = ((a√3)/6)/OB

OB = (a√3)/3

For the triangle of side a, the distance from the centre of mass to the vertex is (a√3)/3.