Q5.    A rhombus shaped field has green grass for 18 cows to graze. If each side of the rhombus is 30 m and its longer diagonal is 48 m, how much area of grass field will each cow be getting?

Answers (1)

To find the area of the rhombus:

We first join the diagonal AC of quadrilateral ABCD.  (See figure)

 

 

 

 

 

 

Here, the sides of triangle ABC are,

a = 30\ m,\ b = 30\ m\ and\ c = 48\ m.

So, the semi-perimeter of the triangle will be:

s = \frac{a+b+c}{2} = \frac{30+30+48}{2} = \frac{108}{2} = 54\ m

Therefore, the area of the triangle given by the Heron's formula,

Area = \sqrt{s(s-a)(s-b)(s-c)}

            = \sqrt{54(54-30)(54-30)(54-48)}

           = \sqrt{54(24)(24)(6)} = \sqrt{186624} = 432\ m^2

Hence, the area of the quadrilateral will be:

= 2\times 432\ m^2 = 864\ m^2

Therefore, the area grazed by each cow will be given by,

= \frac{Total\ area}{Number\ of\ cows} = \frac{864}{18} = 48\ m^2.

 

 

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