Question

the shape of a piece is pallelogram whose adjacent side are 12m and 9 m and the corresponding diagonal is 15 .find the area of land​

Answer 1

Answer: The area of land =108 m²

Explanation:

In the given piece of land is in the shape of a parallelogram.

Diagonals divide it into 2 equal parts.

So, area of parallelogram = 2 x (Area of triangle with sides 12m and 9 m and 15 m)

Heron's formula :

Area of triangle =
`√(s(s-a)(s-b)(s-c))`, where
`s=(a+b+c)/(2)`

Let a= 12 , b= 9 and c = 15

`s=(12+9+15)/(2)=18`

Area of triangle =
`√(18(18-12)(18-9)(18-15))`

`=√(18*6*9*3)=√(2916)=54\ m^2`

Then, area of parallelogram= 2 x 54 = 108 m²

Hence, the area of land =108 m²