Prove the relation between pressure, force and area. P= F/A

Let us suppose force F is applied normally to an area of A and pressure P is produced which is shown in figure. 

We know that , 

pressure is directly proportinal to force applied for constant area. 

that is P∝F ........... (i) 

pressure is inversely proportional to the area A of a contact for a constant force applied. 

P ∝ 1/A  .......... (ii)

Combining the equation from the above statements (i) and (ii) 

We get , 

P∝ F/A 

or P= kF/ A where k is the proportionality constant and its value is 1 in unit system. 

P= 1F/A

P = F/A 

Hence proved.