Pick's Theorem -- Page 12

So each boundary point seems to add ¹/₂ to the area. Let us denote by "B" the number of boundary points and by "I" the number of interior dots. Then we may speculate that the area is related to the number

^B/₂ + I so we compare this to the areas in our original chart.

Figure A B C D E F G H I J K L M N

B 10 10 10 11 12 3 3 4 4 4 6 5 18 12

I 2 3 4 3 3 0 0 0 1 2 0 0 0 5

B/2+I 7 8 9 8.5 9 1.5 1.5 2 3 4 3 2.5 9 11

Area 6 7 8 7.5 8 0.5 0.5 1 2 3 2 1.5 8 10

Figure	A	B	C	D	E	F	G	H	I	J	K	L	M	N
B	10	10	10	11	12	3	3	4	4	4	6	5	18	12
I	2	3	4	3	3	0	0	0	1	2	0	0	0	5
B/2+I	7	8	9	8.5	9	1.5	1.5	2	3	4	3	2.5	9	11
Area	6	7	8	7.5	8	0.5	0.5	1	2	3	2	1.5	8	10