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.
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.