Solution: Let `ABCD` be the field.
Perimeter `= 400 m`
So, each side `= 400 m ÷ 4 = 100 m`
i.e. `AB = AD = 100 m`.
Let diagonal `BD = 160 m`.
Then semi-perimeter `s` of `Delt ABD` is given by
`s = (100 + 100 + 160)/2 m = 180 m`
Therefore, area of `Delta ABD = sqrt ( 180 (180-100)(180-100)(180-160) )`
`= sqrt ( 180 xx 80 xx 80 xx 20) m^2 = 4800 m^2`
Therefore, each of them will get an area of `4800 m^2`.
`text (Alternative method :)` Draw `CE ⊥ BD `(see Fig. 12.14).
As `BD = 160 m`, we have
`DE = 160 m ÷ 2 = 80 m`
And, `DE^2 + CE^2 = DC^2`, which gives
`CE = sqrt (DC^2 -DE^2)`
or, `CE = sqrt (100^2 - 80^2) m = 60 m`
Therefore, area of `Delta BCD = 1/2 xx 160 xx 60 m^2 = 4800 m^2`