Question

The area of a regular hexagon is 2048√3 cm². What is the length (in cm) of each side of the hexagon?

• A. 32√3
• B. 64√3 / 3
• C. 32√3 / 3
• D. 64√3

Answer 1

Answer:

B. 64√3 / 3

For a regular hexagon, the area is given by:

$A = \frac{3\sqrt{3}}{2} a^2$

Given:
$\frac{3\sqrt{3}}{2} a^2 = 2048\sqrt{3}$

Cancel $(\sqrt{3})$ on both sides:
$\frac{3}{2} a^2 = 2048$

$a^2 = \frac{2048 \times 2}{3} = \frac{4096}{3}$
$a = \sqrt{\frac{4096}{3}} = \frac{64}{\sqrt{3}} = \frac{64\sqrt{3}}{3}$

Final Answer: $(\frac{64\sqrt{3}}{3}) cm$