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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?
Answer :

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Let ABCD be a rhombus.

Area of the rhombus ABCD
= 2 × area of ?ABD ... (i)

As we know that, in a rhombus, diagonals divides it in two equal parts.

In ?ABD, we have,
AB = 30 m, BD = 48 m, DA=30 m

Now, we know that,

s=AB+BD+AD2
? s=30+48+302=1082=54m

Now, Area of triangle
= 54(54?30)(54?48)(54?30)
(Since, Heron's formula [area = s(s?a)(s?b)(s?c)])

= 54×24×6×24
= 9×6×4×6×6×4×6
= 3×6×6×4m2
= 432m2

Thus, from Equation (i),

Area of rhombus
= 2 × 432m
= 864 m

Also, Number of cows = 18

So, therefore, Area of grass field per cow
= 86418 = 48m2.