Mathematics - Properties of Triangle Question with Solution | TestHub

A regular hexagon can be divided into 6 congruent equilateral triangles, with their common vertex at the center of the circle. The side length of each equilateral triangle is equal to the radius $R$ of the circumscribing circle. The area of one equilateral triangle with side length $R$ is given by the formula $\frac{\sqrt{3}}{4}{R}^2$. Therefore, the total area of the regular hexagon is $6\times \frac{\sqrt{3}}{4}{R}^2=\frac{3\sqrt{3}}{2}{R}^2$.