Question

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

Answer 1

Let ABCD is a rhombus and length of each side is 30

Length of diagonal AC is 48

From Δ ABC,

Let AB =a =30

AC = b =48

BC = c = 30

Now s = (a+b+c)/2

=> s = (30+48+30)/2

=> s = 108/2

=> s = 54 m

Now area of Δ ABC = √{s*(s-a)*(s-b)*(s-c)}

                             = √{54*(54-30)*(54-48)*(54-30)}

                             = √{54*24*6*24}

                             = √{9*6*24*6*24}

                             = 3*6*24

                             = 432 m2

Area of rhombus ABCD = 2*  area of Δ ABC      (since area of Δ ABC = area of Δ ACD)

                                   = 2* 432

                                   = 864 m2

Now area of grash for 18 cows = 864 m2

So area of grash for 1 cows = 864/18 m2 = 48 m2