If A is area of regular hexagon of side 4 cm, then value of 4A (in cm…

The correct answer is Option (4) → 96\(\sqrt{3}\)

Lines from the centre to the six corners divide a regular hexagon into six equilateral triangles, each with the same side as the hexagon, so the hexagon’s area is six times the area of one such triangle, \(\frac{\sqrt{3}}{4}a^{2}\).

• Area of one triangle of side 4 cm: \(\displaystyle\frac{\sqrt{3}}{4}\times4^{2}=4\sqrt{3}\,\mathrm{cm}^{2}\)

• Area of the hexagon, six such triangles: \(A=6\times4\sqrt{3}=24\sqrt{3}\,\mathrm{cm}^{2}\)

• The question asks for four times this area: \(4A=96\sqrt{3}\,\mathrm{cm}^{2}\)