what is the no. of possible parellelograms? A parallelogram having an acute angle of 30 degrees whose area is equal to the perimeter and the sides are whole numbers then number of such parallelograms possible are?

We interpret the question to mean that we want to find the number of (unordered) pairs $a$, $b$ of integers that can be the sides. The perimeter is $2a+2b$. The area is twice the area of the triangle we get by joining the two vertices at which there is a $150^\circ$ angle. 
The area of each of these triangles is $(1/2)(ab)(\sin 30^\circ)$, for a total of $(1/2)ab$. So we are looking at the equation $2a+2b=(1/2)(ab)$, or equivalently $ab=4a+4b$.
This equation can be rewritten as $(a-4)(b-4)=16$.  Thus $a-4$ and $b-4$ must have product $16$. Without loss of generality we may assume that $a\le b$.
It is easy to see that $a-4$ and $b-4$ cannot both be negative. So $a-4=1$, $b-4=16$, or $a-4=2$, $b-4=8$, or $a-4=4$, $b-4=4$. 
That gives three parallelograms: one with sides $5$ and $20$; another with sides $6$ and $12$;  and finally the rhombus with sides $8$ and $8$. 
