In an regular hexagon inscribed in a circle, its side is equal the radius.
We can divide the hexagon in 6 triangles each with the base of 4. The heigth will equal \sqrt{4^2-2^2}=\sqrt{12}=2\sqrt{3}. To obtain this just use Pythagoras, the hypotenuse of each triangle it's the radius, and the bases it's \frac{4}{2}=2.
Now you have the height of each triangle, so A_t=(4*2\sqrt{3})/2=4\sqrt{3}.
A_h=6*A_t=6*4\sqrt{3}=24\sqrt{3}
We can divide the hexagon in 6 triangles each with the base of 4. The heigth will equal \sqrt{4^2-2^2}=\sqrt{12}=2\sqrt{3}. To obtain this just use Pythagoras, the hypotenuse of each triangle it's the radius, and the bases it's \frac{4}{2}=2.
Now you have the height of each triangle, so A_t=(4*2\sqrt{3})/2=4\sqrt{3}.
A_h=6*A_t=6*4\sqrt{3}=24\sqrt{3}