
★ 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, for which she divides the land in two equal parts.
★ Perimeter of land = 400 m.
★ One of the diagonal = 160 m.

★ Area each of them [son and daughter] will get.

Let, ABCD be the rhombus shaped field and each side of the field be 
[ All sides of the rhombus are equal, therefore we will let the each side of the field be
]
Now,
• Perimeter = 400m





Each side of the field = <u>100m</u><u>.</u>
Now, we have to find the area each [son and daughter] will get.
So, For
ABD,
Here,
• a = 100 [AB]
• b = 100 [AD]
• c = 160 [BD]
![\therefore \tt Simi \: perimeter \: [S] = \boxed{ \sf \dfrac{a + b + c}{2} }](https://tex.z-dn.net/?f=%20%5Ctherefore%20%5Ctt%20Simi%20%5C%3A%20%20perimeter%20%5C%3A%20%20%5BS%5D%20%3D%20%20%5Cboxed%7B%20%5Csf%20%5Cdfrac%7Ba%20%2B%20b%20%2B%20c%7D%7B2%7D%20%7D)



Using <u>herons formula</u><u>,</u>

where
• s is the simi perimeter = 180m
• a, b and c are sides of the triangle which are 100m, 100m and 160m respectively.
<u>Putt</u><u>ing</u><u> the</u><u> values</u><u>,</u>







Thus, area of
ABD = <u>4800 m²</u>
As both the triangles have same sides
So,
Area of
BCD = 4800 m²
<u>Therefore, area each of them [son and daughter] will get = 4800 m²</u>

★ Figure in attachment.
