Question

Find the area of a regular hexagon with side length 4 cm.

• A. $22\sqrt{3}c{m}^2$
• B. $24\sqrt{3}c{m}^2$
• C. $24\sqrt{2}c{m}^2$
• D. $20\sqrt{3}c{m}^2$

Answer 1

The correct option is B

$24\sqrt{3}c{m}^2$

Given regular hexagon has side 4 cm.

We can split the given regular hexagon into 6 equilateral triangles.

Area of equilateral triangle $=\frac{\sqrt{3}}{4}sid{e}^2$

Area of hexagon $=6\times \frac{\sqrt{3}}{4}sid{e}^2$

$=\frac{3\sqrt{3}}{2}\times sid{e}^2$

$=\frac{3\sqrt{3}}{2}\times 4\times 4$

$=24\sqrt{3}c{m}^2$