Question 54

The area of a field in the shape of a hexagon is 2400 $$\sqrt3 m^2$$. What will be the cost of fencing it at ₹18.50 per metre?

Solution

The area of a field in the shape of a hexagon is 2400 $$\sqrt3 m^2$$.

area of hexagon = $$\frac{3\sqrt{\ 3}\times\left(side\right)^2}{2}$$

$$2400\sqrt3 = \frac{3\sqrt{\ 3}\times\left(side\right)^2}{2}$$

$$800=\frac{\left(side\right)^2}{2}$$

$$(side)^2 = 1600$$

side = 40

perimeter of hexagon = $$6\times side$$

= $$6\times 40$$

= 240 metre

Cost of fencing it at ₹18.50 per metre = $$240\times ₹18.50$$

= ₹4440

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