Pick's Rule for Area

1. Teacher Demo Polygon

Count carefully: a corner counts once, and any dot touching the edge is a boundary point.

B Boundary points

I Interior points

A Area in square units

Record the teacher's result:

B =

I =

A =

2. Investigation Figures

For each figure, count B, count I, and calculate the area A using any method you already know.

Figure asquare

B =

I =

A =

Figure bsquare

B =

I =

A =

Figure ctriangle

B =

I =

A =

Figure dirregular polygon

B =

I =

A =

Figure eirregular polygon

B =

I =

A =

Figure firregular polygon

B =

I =

A =

3. Summary Table

Figure	B	I	A
demo polygon
a
b
c
d
e
f

4. Pattern Hunt

After the first two rows, write a guess for a relationship between B, I, and A.
Test your guess against the other rows. If it fails, revise it.
Write the final rule only when you are convinced it works for all the figures.

My first guess:

After testing:

5. Classwork Check - Verify the Rule on Your Own Polygon

Draw your own lattice polygon on the blank grid. Make it at least 5 sides and not a rectangle. Then count B, count I, use Pick's Rule to predict the area, and verify the area by decomposition or square-counting.

B =

I =

Pick's Rule area =

Checked by decomposition / square-counting:

6. Final Statement

Write Pick's Rule in words:

Write it as a formula: A =