# Convergence of Area

To get a better approximation of the area of Minnesota, we need to use a
finer grid. Rather than count squares ourselves, we will have the computer
decide that a square is within the boundary if its lower left corner is within
the state boundaries. The approximate area will be the sum of the areas of
the squares contained within the state.

## Question #2

- Use the Maple command

` MNleftbox(1,grid=[10,10]);`

to compute an approximate are of MN. Can you explain why this answer
is different from your answer to Question #1?
- Increase your grid size to 15 by 15 and then 20 by 20 and recompute
approximate areas. Use the data you've collected to estimate
the area of the model. (Explain how you arrived at your conclusion.)

## Question #3

Answer this question at home.
- The Southern border of Minnesota is about 250 miles
long and the distance from the southern border to Canada is
approximately 375 miles.
Use these facts to determine the horizontal and vertical scale of the
model that we are using.
- Use your data to approximate the actual total land area
(in square miles) of Minnesota. Consult an atlas, almanac, or encyclopedia
to find the actual land area of Minnesota. Based on these facts,
do you think the model of Minnesota that we are using is a good model?

**Next: **Integrating Density Distributions

**Up: **Introduction

**Previous: **The Area of Minnesota

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

Last modified: Fri Feb 3 11:43:54 1995