# The Area of Minnesota

In Lab 12 we numerically approximated the area of planar regions defined by some equations or set of equations. This section asks the question: what do we do if we do not have a formula for the region of interest?

The basic geometric idea is the same as it was in the previous lab: impose a grid on the region and count the number of boxes falling within the region. As the grid becomes finer and finer, the area of the boxes within the region will typically approach the actual area of the region.

We illustrate this geometric picture by formulating a model for the state of Minnesota. First, you must read in some Maple commands:

`read `/u/calcIII/MVCalc.define`;`

We model the state of Minnesota as the region enclosed by it's east and west borders (approximated by a set of data points connected by linear segments) and it's north and south borders (approximated by straight lines).

## Question #1

• Issue the maple command:
`MNgridplot(10,10);`
to see the model that we are using. Compare this model to the actual map that you were given. How is the model different from reality? Do you think our model is a reasonable approximation of reality? Why or why not?
• Estimate the area of our model by using the 10x10 grid. What method do you use to decide which boxes are inside Minnesota?

Next: Convergence of Area
Previous: Introduction

Frederick J. Wicklin <fjw@geom.umn.edu>
Brian Burt
Document Created: Fri Jan 27 CST