Geometry Help
Given a simple polygon constructed on a grid of equal-distanced points (i.e., points with integer coordinates) such that all the polygon's vertices are grid points, Pick's theorem provides a simple formula for calculating the area A of this polygon in terms of the number i of lattice points in the interior located in the polygon and the number b of lattice points on the boundary placed on the polygon's perimeter:
i = 7, b = 8,
A = i + b/2 − 1 = 10
see: https://en.wikipedia.org/wiki/Pick%27s_theorem
1. What is the area of this polygon?
i=33b=20A=33+202−1A=42
2. What is the area of this polygon?
i=34b=21A=34+212−1A=43.5
4. This figure is made up of a rectangle and parallelogram.
What is the area of this figure?
i=18b=18A=18+182−1A=26