Hi Ranjit,

No there isn't something like a Heron's formula for the situation you describe.

In fact, even with Heron's formula, you need to know the actual lengths of the sides, not just the total perimeter.

An irregular pentagon can have an infinite number of shapes with an infinite number of different areas - even if the perimeter is held constant (think of a pentagon that is almost regular and then think of one that is really flattened, for example). The reason Heron's formula works is that knowing the lengths of the three sides of a triangle fully defines all the angles and lengths. Even if you knew all the lengths of the sides of an irregular pentagon, you wouldn't know the shape.

Stephen La Rocque.>