Question : The area of a field in the shape of a hexagon is $1944 \sqrt{3} \mathrm{~m}^2$. What will be the cost (in INR) of fencing it at the rate of 11.50 per metre?
Option 1: 2,785
Option 2: 2,484
Option 3: 3,200
Option 4: 2,256
Correct Answer: 2,484
Solution :
Area of the hexagon field = 1944$\sqrt{3}$ m$^2$
The rate of fencing the area = 11.50 per metre
Area of the regular hexagon is $3\sqrt{3} × (\frac{a^2}{2})$ and its perimeter is $6a$,
where $a$ is the side of the regular hexagon.
Cost of the fencing = $6a$ × rate per metre
Substituting the values in the formula
$3\sqrt{3} × (\frac{a^2}{2}) = 1944\sqrt{3}$
⇒ $a$ = 36 m
The perimeter of the hexagon = $6a$ = 6 × 36 = 216 m
Cost of fencing = 216 × 11.50 = INR 2,484
$\therefore$ Cost of fencing field in a hexagon shape is INR 2,484.
Hence, the correct answer is 2,484.
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