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If area of the hexagon is 24√3cm², find its perimeter.
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[tex]\huge\tt{\fcolorbox{purple} {lavenderblush}{{Question }}}[/tex]
If area of the hexagon is 24√3cm², find its perimeter.
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To,luckymurmu07
To find the perimeter of a hexagon, we need to know more about its properties. However, we can calculate the side length (s) of a regular hexagon using the given area.
The area of a regular hexagon can be expressed as:
\[ \text{Area} = \frac{3\sqrt{3}}{2} \times s^2 \]
Given that the area is \( 24\sqrt{3} \, \text{cm}^2 \), we can set up an equation:
\[ 24\sqrt{3} = \frac{3\sqrt{3}}{2} \times s^2 \]
Now, solve for \( s \):
\[ s^2 = \frac{2 \times 24\sqrt{3}}{3\sqrt{3}} \]
\[ s^2 = 16 \]
\[ s = 4 \]
Now that we know the side length (\( s = 4 \)), we can find the perimeter (\( P \)) of the hexagon using the formula for the perimeter of a regular hexagon:
\[ P = 6s \]
\[ P = 6 \times 4 \]
\[ P = 24 \]
Therefore, the perimeter of the hexagon is \( 24 \) cm.