Question

Question 5
A rhombus shaped field has green grass for 18 cows to graze. If each side of the rhombus is 30m and its longer diagonal is 48m, how much area of grass field will each cow be getting?

Answer 1

Let ABCD be a rhombus-shaped field.
For $\Delta BCD$,
Semi-perimeter, $s=\frac{(48+30+30)}{2}=54m$
By Heron's formula,
Area of triangle = $\sqrt{s(s-a)(s-b)(s-c)}$
Therefore the area of
$\Delta BCD=\lfloor \sqrt{54(54-48)(54-30)(54-30)}\rfloor m^2=\sqrt{54\left(6\right)\left(24\right)\left(24\right)}=432m^2$
Area of field = 2 $\times$ Area of $\Delta BCD$
$=(2\times 432)m^2=864m^2$
Area of grazing for 1cow = $\frac{864}{18}=48m^2$
Each cow will get $48m^2$ area of grassfield.