JAMB 1985 · UME · Q36

Find the area of a regular hexagon inscribed in a circle of radius 8 cm.

Worked solution (try it first)

Joining the centre to the six corners splits the hexagon into six equilateral triangles, each of side 8 cm (the radius).
One triangle has area $\frac{\sqrt3}{4} \times 8^2 = 16\sqrt3\text{ cm}^2$ .
The hexagon is six of them: $6 \times 16\sqrt3 = 96\sqrt3\text{ cm}^2$ , option B.