Q. 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?

Explanation

Let `ABCD` be a rhombus of side 30m
`AB=BC=CD=DA=30m`
Also,diagonal`=48m=BD`
Area of rhmbus`=ar/_\ABD+Area/_\BCD`
ar of `/_\ABD= sqrt(s(s−a)(s−b)(s−c))`
`s=1/2(a+b+c)`
`=>1/2(30+30+48)=54cm`
ar of `/_\ABD=sqrt(s(s−a)(s−b)(s−c))`
Here,`a=30m,b=30m ,c=48m and s=54`
`=sqrt(54(54−30)(54−30)(54−48))`
`=>sqrt(54xx24xx24xx6)=432m^2`
Hence Area of `/_\ABD=432m^2`
As both `/_\ABD \and\ /_\BCD` have the same sides
ar`/_\BCD=432 m^2`
So, Area of rhombus,`ABCD=432+432=864m^2`
Thus, Area of Rhombus`=864m^2`
Given that 18 cows to graze the field.
So, Area of 18cows=(Area of the rhombus).
Area of Each cow`=864/18=48m^2`
Thus, each cow will get`48m^2`,area of the grass field.