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 :)