Question

A regular hexagon has a side 6cm. Its area is:

• A. $8\sqrt{3}c{m}^2$
• B. $10\sqrt{2}c{m}^2$
• C. $11\sqrt{2}c{m}^2$
• D. $54\sqrt{3}c{m}^2$

Answer 1

The correct option is D

$54\sqrt{3}c{m}^2$

Side = 6 cm
ABCDEF is a regular hexagon. Join diagonals AD, BE and CF. The three diagonal divides the hexagonal in six congruent equilateral triangle with side 6cm.
Area of one such triangle.
$=\sqrt{s(s-a)(s-b)(s-c)}$

where $s=\frac{6+6+6}{2}$ = 9
$=\sqrt{9(9-6)(9-6)(9-6)}=\sqrt{9\times 3\times 3\times 3}$
$=9\sqrt{3}$
$\therefore$ Area of the regular hexagon
= 6 $\times$ Area of equilateral triangle OAB

$=6\times 9\sqrt{3}=54\sqrt{3}c{m}^2$