how to find are of frequency polygon

Consider a frequency polygon as shown in the figure above.

Its area can be find out by dividing the graph in terms of squares, rectangles, triangles, parallelograms, trapezium whichever shape is possible and whose area can easily be find out.

In the figure shown below, the given frequency polygon is divided into number of figures mainly rectangles and triangles as: 

Therefore, area of given frequency polygon = Ar(Δ PQB) + Ar(Δ BFE) + ar(FERQ) + ar(Δ BCE) + ar(Δ DCE) + ar(Δ ERS)

From the graph dimension of each side can easily be find out and by using the Heron's formula  for triangle and area of rectangle = length × breadth of rectangle we can easily find out the area of frequency polygon by adding all respective areas.

Hope you get it!!