Sanya has a piece of land which is in the shape of a rhombus. She wants her one daughter and one son to work on the land and produce different crops to suffice the needs of their family. She divided the land in two equals parts. If the perimeter of the land is `400 m` and one of the diagonals is `160 m ,` how much area each of them will get?

Explanation

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 `/_\ ABD` is given by
`s =(100+100+160)/2` `m`
`= 180 m`
Therefore, area of `/_\ ABD = sqrt(180(180-100) (180 - 100) (180 - 160))`
`= sqrt(180xx80xx80xx20)` `m^2`
`= 4800 m^2`
Therefore, each of them will get an area of `4800 m^2`
.