The area of a regular triangle is √3 / 3. Find the length of its bisector

The bisector of an equilateral triangle is both its height and median. If a is a side of a triangle, then its height h = | ВD | from a right-angled triangle ABD is equal to:

h = a sin (π / 3) = a * √3 / 2;

and for the area S we get:

S = (1/2) * a * h = (1/2) * a * a * (√3 / 2) = a ^ 2 * √3 / 4;

By the condition of the problem:

S = a ^ 2 * √3 / 4 = √3 / 3;

a ^ 2 = 4/3;

a = 2 / √3;

Accordingly, the bisector and the height of the triangle are:

h = a * √3 / 2 = (2 / √3) * (√3 / 2) = 1.

Answer: the bisector is 1.