The area of a regular hexagon is 2048
The area of a regular hexagon is 2048\(\sqrt{3}\) cm\(^2\). What is the length(in cm) of each side of the hexagon?
एक सम षट्भुज का क्षेत्रफल 2048\(\sqrt{3}\) cm\(^2\) है। षट्भुज की प्रत्येक भुजा की लंबाई (cm में) ज्ञात करें?
Detailed Solution & Logic
\(\frac{64\sqrt{3}}{3}\)
A regular hexagon is made of 6 equilateral triangles
Area of one equilateral triangle = $ \frac{\sqrt{3}}{4}a^2 $
Area of hexagon = $ 6 \times \frac{\sqrt{3}}{4}a^2 = \frac{3\sqrt{3}}{2}a^2 $
Given area = $ 2048\sqrt{3} $
$ \frac{3\sqrt{3}}{2}a^2 = 2048\sqrt{3} $
$ \frac{3}{2}a^2 = 2048 $
$ a^2 = \frac{4096}{3} $
$ a = \sqrt{\frac{4096}{3}} = \frac{64}{\sqrt{3}} = \frac{64\sqrt{3}}{3} $
Correct option: $\frac{64\sqrt{3}}{3}$
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