Question

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 1

Let the longer diagonal divides the rhombus ABCD into two congruent angles.
For ∆ABC, a = b = 30 m, c = 48 m
And Semi Perimeter(s) = $\frac{a+b+c}{2}$= 54 m
Area of ΔABC = $\sqrt{s(s-a)(s-b)(s-c)}=\sqrt{54(54-30)(54-30)(54-48)}=\sqrt{54\times 24\times 24\times 6}$
Area of ΔABC = 432 m²
Area of rhombus = 2 × Area of a ΔABC
= 2 × 432 m²
= 864 m²
Since, number of cows = 18
The area of grass field will each cow get $=\frac{\text{Total area of the rhombus}}{18}=\frac{864}{18}=48m^2$