Question

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

• A. $27\sqrt{3}c{m}^2$
• B. $10\sqrt{2}c{m}^2$
• C. $9\sqrt{2}c{m}^2$
• 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.
Using Heron's formula area of triangle is given by
Area of one such triangle.
$=\sqrt{s(s-a)(s-b)(s-c)}$
$=\sqrt{9(9-6)(9-6)(9-6)}=\sqrt{9\times 3\times 3\times 3}$
$=9\sqrt{3}$
$\therefore$ Area of the regular hexagon
= 6 $\times$ Area of equilateral triangle OAB

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