__Pick’s Theorem__
This
formula was created by Georg Alexander
Pick in 1899.

Using
the Geoboard to Assist :

·
Draw a polygon on the Geoboard

·
Determine the number of boundary points
and the number of interior points and calculate its area

·
Repeat with different polygons

·
Draw polygons without any interior
points and find the area

·
Draw polygons with one interior point
and find the area

·
Draw polygons with two interior points
and find the area

·
Prepare a table with number of boundary
points, number of interior points, and area. Discover that the relationship
between B the number of boundary points, i the number of internal points, and
the area of the geoboard polygon is given by Pick's formula

**A = I + ½ B – 1**

**The diagram below explains this further.**

I understand this better now! Wow :)

Marina Ho

BSc08