Question

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

Given

ABCD is a rhombus having diagonal AC

side $AB=BC=CD=AD=30cm$

The diagonal of the Rhombus divides the area into two equal parts.

Find out

We have to determine how much area of grass field will each cow be getting

Solution

Using Heron’s formula, area of the triangle =$\sqrt{s\left(s-a\right)\left(s-b\right)\left(s-c\right)}$

Now, $ar\left(△ABC\right)$ can be calculated by Heron’s Formula, where

AB $=$ $a$ $=$$30cm$

BC $=$$b$$=$$30cm$

AC $=$ $c$ $=$$48cm$

Semi Perimeter $\left(s\right)=\frac{a+b+c}{2}$

$$\begin{gathered} s=\frac{30+30+48}{2} \\ s=\frac{108}{2} \\ s=54m \end{gathered}$$

$ar\left(△ABC\right)$ $=$$\sqrt{s\left(s-a\right)\left(s-b\right)\left(s-c\right)}$

$$\begin{gathered} =\sqrt{54\left(54-30\right)\left(54-30\right)\left(54-48\right)} \\ =\sqrt{54\times 24\times 24\times 6} \\ =432m^2 \end{gathered}$$

Hence, the Area of rhombus $=$$2\times ar\left(△ABC\right)$

$$\begin{gathered} =2\times 432 \\ =864m^2 \end{gathered}$$

Area for $18$ cows $=$$864m^2$

Area for each cow $=$ $\frac{864}{18}$$=$$48m^2$

Therefore, area for each cow $48m^2$.