Question

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

• A. 52. 54 $c{m}^2$
• B. 41.56 $c{m}^2$
• C. 46.62 $c{m}^2$
• D. 56.62 $c{m}^2$

Answer 1

The correct option is B

41.56 $c{m}^2$

Given, regular hexagon has each side of length 4 cm.
We can divide a regular hexagon into 6 equilateral triangles.
Area of an equilateral triangle
$=\frac{\sqrt{3}}{4}{\text{(side)}}^2$
Hence, area of the hexagon
$=6\times \frac{\sqrt{3}}{4}\text{(side}{)}^2$
$=\frac{3\sqrt{3}}{2}\times \text{(side}{)}^2$
$=\frac{3\sqrt{3}}{2}\times 4^2$
$=41.56{\text{cm}}^2$