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

Answer:

Let ABCD be a rhombus of side 30m

AB=BC=CD=DA=30m

Also, diagonal=48m

BD=48m

Area of rhmbus=Area△ABD+Area△BCD

For △ABD,

Area of triangle=  

s(s−a)(s−b)(s−c)

​

 

Here,s is the semi perimeter, and a,b,c are the sides of the triangle.

Here a=30m,b=30m and c=48m

S=  

2

a+b+c

​

=  

2

30+30+48

​

=  

2

108

​

=54m

Area of △ABD=  

s(s−a)(s−b)(s−c)

​

 

Here a=30m,b=30m ,c=48m and s=54,

=  

54(54−30)(54−30)(54−48)

​

=  

54×24×24×6

​

=432m  

2

 

Hence Area of △ABD=432m  

2

 

As both △ABD and △BCD have the same sides,

Area of △BCD=432 m  

2

 

So, Area of rhombus ABCD

= Area of △ABD + Area of △BCD=432+432=864m  

2

 

Thus, Area of Rhombus=864m  

2

 

Given that 18 cows to graze the field.

So, Area of 18 cows=Area of the rhombus.

Area of Each cow=  

18

Areaofrhombus

​

=  

18

864

​

=48m  

2

 Thus, each cow will get 48m  2 area of the grass field.

Answer 2

Let ABCD be a rhombus of side 30m

AB=BC=CD=DA=30m

Also, diagonal=48m

BD=48m

Area of rhmbus=Area△ABD+Area△BCD

For △ABD,

Area of triangle=

s(s−a)(s−b)(s−c)

Here,s is the semi perimeter, and a,b,c are the sides of the triangle.

Here a=30m,b=30m and c=48m

S=

2

a+b+c

=

2

30+30+48

=

2

108

=54m

Area of △ABD=

s(s−a)(s−b)(s−c)

Here a=30m,b=30m ,c=48m and s=54,

=

54(54−30)(54−30)(54−48)

=

54×24×24×6

=432m

2

Hence Area of △ABD=432m

2

As both △ABD and △BCD have the same sides,

Area of △BCD=432 m

2

So, Area of rhombus ABCD

= Area of △ABD + Area of △BCD=432+432=864m

2

Thus, Area of Rhombus=864m

2

Given that 18 cows to graze the field.

So, Area of 18 cows=Area of the rhombus.

Area of Each cow=

18

Areaofrhombus

=

18

864

=48m

2