Find the length of a circle if the area of a regular hexagon inscribed in it is 72√2 cm ^ 2.

To complete this task, you need to find the circumference;

Let’s consider this condition and analyze it.

According to the condition of the task, we are given a circle with an inscribed hexagon of regular shape, and the area of this hexagon is also known.

Let’s write down the formula for a regular hexagon;

S = (3 * √3 * a ^ 2) / 2;

From this formula we find the side of the hexagon “a”;

a ^ 2 = (2 * S / 3 * √3);

a ^ 2 = (2 * 72 * √2 / 3 * √3);

a ^ 2 = 48;

Since the side of the hexagon is equal to the radius of the circle, we find the length of the circle;

L = 2 * P * r;

L = 6.28 * √48.