Centre of gravity (centroid) of an equilateral triangle: distance from any side An equilateral triangular lamina has side length a. Choose the correct perpendicular distance of the centroid from any of its sides.

Given data

• Equilateral triangle, side a.

Concept/Approach

• Height h of an equilateral triangle is h = (√3/2)·a.
• The centroid divides the height in the ratio 2:1 from vertex to base, so its distance from a side (the base) equals h/3.

Step-by-step calculation
Distance from any side = h/3 = [(√3/2)·a]/3 = (√3 a)/6.

Common pitfalls

• Confusing centroid with incenter or circumcenter distances; only the centroid gives h/3 from each side.

Final Answer
(√3 a)/6