Question : ABCDEF is a regular hexagon. The side of the hexagon is 36 cm. What is the area of the $\triangle ABC$?
Option 1: $324 \sqrt{3}\ {cm}^2$
Option 2: $360 \sqrt{3} \ {cm}^2$
Option 3: $240 \sqrt{3} \ {cm}^2$
Option 4: $192 \sqrt{3} \ {cm}^2$
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Correct Answer: $324 \sqrt{3}\ {cm}^2$
Solution :
Given: ABCDEF is a regular hexagon.
The side of the hexagon is 36 cm.
The area of the regular hexagon of side $a$ is $6\times \frac{\sqrt3}{4}a^2$.
A regular hexagon is divided in to six equal triangles.
So, the area of the $\triangle ABC$ $=\frac{1}{6}\times 6\times \frac{\sqrt3}{4}a^2$.
⇒ $\frac{1}{6}\times 6\times \frac{\sqrt3}{4}\times (36)^2=324 \sqrt3 \ cm^2$
Hence, the correct answer is $324\sqrt3 \ cm^2$.
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