The area of a regular hexagon in this case is:
S = (3 √3 * r²) / 2, where r is the radius of the circumscribed circle.
It remains to find the radius. It is known that the area of a circle is equal to 36π, and it is calculated by the formula
S = πr²,
r = √S / π.
Now r can be found:
r = √36π / π = √36 = 6.
We found the radius, then we look for the area of the hexagon:
S = (3√3 * 6²) / 2 = (3√3 * 36) / 2 = 3√3 * 18 = 54√3.
Answer: the area of a regular hexagon is 54√3.
One of the components of a person's success in our time is receiving modern high-quality education, mastering the knowledge, skills and abilities necessary for life in society. A person today needs to study almost all his life, mastering everything new and new, acquiring the necessary professional qualities.