Question

From Bernoulli's principle it was found that as area decreases velocity increases and pressure at that point decreases. But we also know that pressure is inversely proportional to area[P=F/A]. So it is found that pressure is proportional to the area[Bernoulli], but also pressure is inversely proportional to the area[F/A]. how is that possible?

Answer 1

This area is completely different to the one above", but this means nothing. The equation p=FAp=FA mentioned by the author does hold, and there is no contradiction or paradox in it.

In fact, the equation p=FAp=FA holds not only here but anywhere else in physics. You may write it in any situation, and it will always be true.

Let's begin with a small correction. Your Av=constantAv=constant equation is not Bernoulli, but mere conservation of mass. Here's Bernoulli. This is what gives, in your words, "pressure is inversely proportional to velocity."
pρ+v22+gz=constant
pρ+v22+gz=constant
So your problem is with p=FAp=FA. Well, there's no problem with it. What is really wrong with your thinking is that you're not paying attention to the equation: the force FF changes too.

Let's recap what happens in your situation:

There's a change in cross-sectional area: A2<A1A2<A1
Thanks to conservation of mass, (1) implies v2>v1v2>v1
Thanks to Bernoulli, (2) implies p2<p1