What is the area (in cm2) of a regular hexagon of side 12 cm?
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → \(216\sqrt{3}\)
Joining the centre of a regular hexagon to its six corners splits it into 6 equilateral triangles with the same side as the hexagon. The area of an equilateral triangle of side \(a\) is \(\displaystyle \frac{\sqrt{3}}{4}a^2\).
Area of one triangle \(\displaystyle =\frac{\sqrt{3}}{4}\times12^2=\frac{\sqrt{3}}{4}\times144=36\sqrt{3}\) cm2
Area of the hexagon \(=6\times36\sqrt{3}=216\sqrt{3}\) cm2
