(solved)Question 6 SSC-CGL 2020 March 4 Shift 3

A field whose area is 2400√3 sq. m is in the shape of a regular hexagon. If the cost of fencing the field is Rs 16.80/m, then find the total cost required to completely fence the field?
(Rev. 20-Jan-2024)

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Parveen,

Question 6
SSC-CGL 2020 Mar 4 Shift 3

A field whose area is 2400√3 sq. m is in the shape of a regular hexagon. If the cost of fencing the field is Rs 16.80/m, then find the total cost required to completely fence the field?

Solution in Brief

A regular hexagon has 6 equilaterals. Area of 1 equilateral = (2400√3)6 = 40√3. By formula for the area of an equilateral is √3a²/4. Equating, a = 40. So perimeter of the hexagon is 6 x 40 = 240. Cost is 240 x 16.80 = 4032 Rs. answer!

Solution in Detail

This question is based on the formula for the area of a regular hexagon.

Equating, we get

$\displaystyle \frac{3\sqrt 3}{2} a^2 = 2400\sqrt 3$

$\displaystyle \therefore a^2 = 1600$

$\displaystyle \therefore a = 40$ meters.

Perimeter = $\displaystyle 6 \times 40 = 240 $ m

Cost of fencing given $\displaystyle 16.80$ meter

$\displaystyle \therefore$ cost = $\displaystyle 240 \times 16.80$

$\displaystyle = 4032 \:\underline{Ans}$

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