Example 6: Sanya has a piece of land which is in the shape of a rhombu

1.	Example 6: Sanya has a piece of land which is in the shape of a rhombus(see Fig. 12.13). She wants her one daughter and one son to work on the land andproduce different crops. She divided the land in two equal parts. If the perimeter ofthe land is 400 m and one of the diagonals is 160 m, how much area each of them willget for their crops?100 m
Answer» Let ABCD be the field. Given perimeter = 400 m So, each side = 400/4 = 100 m Diagonal BD = 160 m Let a = 100 m, b = 100 m, c = 160 m ∴s = (a + b + c)/2 = (100 + 100 + 160)/2 = 180 m. Therefore, Area of△ABD = root under (√s(s - a)(s - b)(s - c)) =root under (√180(180 - 100)(180 - 100)(180 - 160)) =root under (√180 x 80 x 80 x 20) = 4800 m2

Example 6: Sanya has a piece of land which is in the shape of a rhombus(see Fig. 12.13). She wants her one daughter and one son to work on the land andproduce different crops. She divided the land in two equal parts. If the perimeter ofthe land is 400 m and one of the diagonals is 160 m, how much area each of them willget for their crops?100 m

Answer»

Let ABCD be the field. Given perimeter = 400 m

So, each side = 400/4 = 100 m

Diagonal BD = 160 m

Let a = 100 m, b = 100 m, c = 160 m

∴s = (a + b + c)/2 = (100 + 100 + 160)/2 = 180 m.

Therefore, Area of△ABD = root under (√s(s - a)(s - b)(s - c))

=root under (√180(180 - 100)(180 - 100)(180 - 160))

=root under (√180 x 80 x 80 x 20) = 4800 m2