If the sides of a parallelogram are 100 m each and the length of the longest diagonal is 160 m. Then the area of a parallelogram will be:

Given that the sides of a parallelogram are 100 m and the length of the diagonal is 160 m. And the diagonal divides the parallelogram into two equivalent triangles.

Semiperimeter (s) = (a + b + c)/2 = (100 + 160 + 100)/2 = 360/2 = 180 m

Now, by using Heron’s formula the area of the triangle will be:

$$\begin{gathered} A=\sqrt{s(s-a) (s-b) (s-c)} \\ = \sqrt{180 (180-100) (180-160) (180-100)} \\ =\sqrt{180 \left(80\right) \left(20\right) \left(80\right)} \\ = 4800 m^2 \end{gathered}$$

Thus, the area of the triangle is 4800 sq.m

Now, we know that the diagonal divides the parallelogram into two equivalent triangles and due to this the area of the parallelogram will be equal to the sum of the area of the two triangles. 

Hence, the area of the parallelogram = 2 × 4800 sq.m = 9600 sq.m