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Enrichment

Pick's Method to find the area of irregular figure
Georg Alexander Pick in 1899, formulated a method to find the area of a simple polygon whose vertices are
on lattice points. Let ‘i’ be the number of lattice points interior to polygon, and ‘b’ be the number of lattice points
on its boundary, then the area is given by
b
A =+ −1 .
i
2
For example, consider the area of the given figure.
Here, the number of interior points of the polygon is 7 and the number of points on the
boundary is 8.
8
1
So, Area = 7+− = 10 sq. units
2
Example: Find the area of the figure given below.

Solution: In the above figure, the number of interior points is 1 and the number of boundary points is 96.
96
=
So, Area = 1+ − 148 sq. units
2
Find the area of the following irregular figures.

1. 2. 3.

197
197 Perimeter and Area
and Ar
ea
P
erimeter