Lesson 3: Distances and Areas

Lesson 3:
Distances and Areas

In this lesson, you will determine the area for Morgan, Sedgwick and Bent Counties by measuring the size of each county. You will be able to determine the accuracy of your answer by referring to the ArcView data table. You will also be using conversion factors.

Note: Limited ArcView instructions will be provided in this lesson. Please refer to Lesson 1 for additional ArcView assistance.

If you have not downloaded the data for this lesson, download the data now.

Note to PSD Mac Users:
The Shapefiles (*.shp) and ArcView Project Files (*.apr) for this project are contained in the folder: Mathematics-7th

At this time you may print the Lesson 3 Worksheet to aid you in answering the questions during the lesson.

ArcView Steps for Problem Set 1

Step 1	Open ArcView. Set your Working Directory.
MAC Users:	Start ArcView by selecting: Macintosh HD \| Documents \| ArcView alias \| Open ArcView and select File \| Open Project \| ArcView Projects \| Mathematics-7th \| MathL3.apr Set your Working Directory.
Step 2	To view the data you must display the themes or data layers. Make counties visible by checking the box to the left of the name. With your teacher's permission you may change the colors and symbols displayed in the view.
Step 3	In order for you to have access to the data you must make the data layer active. Make the layer active by clicking on it. The button should appear to be raised.
Step 4	Zoom to the extent of the counties, which is now your active layer. When you zoom to the extent of a theme, you are able to view the entire data layer.

Questions for Problem Set 1

Note: Refer to the Area and Volume section of your textbook.

Question 1 For Question 1 you will determine the approximate area for Sedgwick, Morgan, and Bent Counties located in Colorado.
a) How would you determine area if all you were given was the shape of the county and a unit of measurement?
b) What is the formula used to determine the area of a square?
c) What is the formula used to determine the area of a rectangle?
You will be using the Measure Distance tool to determine the length of county boundaries.
First, Zoom In on Sedgwick County. Click on the Measure Distance tool , a small crosshair and a right angle rule should appear in the view (make sure the cursor is in the view window).
Place the crosshair on a corner of the county. Hit the one button of your mouse and then drag the ruler to the opposite corner and hit the one key of your mouse again.

Note: To reset the Measure Distance tool you must re-click on the icon.
As you drag the crosshair across the screen look in the lower left hand corner of the ArcView window. You should see numbers defined as Segment Length and Length. These indices are measuring the distance the ruler is moving across the map in the map units.
d) What unit of measurement is the map being measured in?
Take a few seconds to get use to the Measure Distance tool.
Now, as precisely as possible use the Measure Distance tool to measure the width and height of the rectangle (Sedgwick County).
Remember to click on the Measure Distance tool each time you measure a new length.
For a precise estimate, record distance as shown in corner of screen. Do not round number.
e) Determine the area for Sedgwick County. Be careful of your units.
You now want to view the entire state. Use the Zoom to extent of all themes button.

Question 2 Determine the area for Morgan County.
Repeat the steps from question one, using the Measure Distance tool and the Zoom In tool.

Question 3 Determine the area for Bent County.
Repeat the steps from question one, using the Measure Distance tool and the Zoom In tool.

Question 4 For Question 4 we will use an ArcView display table to obtain the areas for Sedgwick, Morgan and Bent Counties. Be aware that your measurements were approximate and therefore may not match the ArcView areas exactly. Your area estimates should be within 50 - 100 square miles of ArcView's areas.
Click the Zoom to extent of all themes button.
Use the Identify tool to select and list the ArcView county data. Click the Identify tool on Sedgwick, Morgan, and Bent Counties. Notice how the information in the table changes as you select different counties.
a) What are the ArcView areas displayed in the 'Identify Results' table for Sedgwick, Morgan, and Bent Counties?
b) How do your results for Sedgwick, Morgan, and Bent Counties compare to the ArcView data?

Close the 'Identify Results' table. Click on the in the upper left hand corner of the table and zoom out to full extent of the theme

Question 5 For the last question of Problem Set 1, you will convert the area of Bent County to acres.
Use the ArcView data you recorded from the 'Identify Results' table.
1 square mile = 640 acres
Convert area in square miles for Bent County to acres.

That's all for Problem Set 1 Click on the Unselect All button .
With your teacher's permission you may exit Arcview. Click on File/Exit.

See data Disclaimer

Go to the HELP page

Go to Lesson 1: Introduction to the ArcView Interface and the Data.

Go to Lesson 2: Percentages and Proportions

Go to Lesson 4: Introduction to Statistics

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Question 1	For Question 1 you will determine the approximate area for Sedgwick, Morgan, and Bent Counties located in Colorado. a) How would you determine area if all you were given was the shape of the county and a unit of measurement? b) What is the formula used to determine the area of a square? c) What is the formula used to determine the area of a rectangle? You will be using the Measure Distance tool to determine the length of county boundaries. First, Zoom In on Sedgwick County. Click on the Measure Distance tool , a small crosshair and a right angle rule should appear in the view (make sure the cursor is in the view window). Place the crosshair on a corner of the county. Hit the one button of your mouse and then drag the ruler to the opposite corner and hit the one key of your mouse again. Note: To reset the Measure Distance tool you must re-click on the icon. As you drag the crosshair across the screen look in the lower left hand corner of the ArcView window. You should see numbers defined as Segment Length and Length. These indices are measuring the distance the ruler is moving across the map in the map units. d) What unit of measurement is the map being measured in? Take a few seconds to get use to the Measure Distance tool. Now, as precisely as possible use the Measure Distance tool to measure the width and height of the rectangle (Sedgwick County). Remember to click on the Measure Distance tool each time you measure a new length. For a precise estimate, record distance as shown in corner of screen. Do not round number. e) Determine the area for Sedgwick County. Be careful of your units. You now want to view the entire state. Use the Zoom to extent of all themes button.
Question 2	Determine the area for Morgan County. Repeat the steps from question one, using the Measure Distance tool and the Zoom In tool.
Question 3	Determine the area for Bent County. Repeat the steps from question one, using the Measure Distance tool and the Zoom In tool.
Question 4	For Question 4 we will use an ArcView display table to obtain the areas for Sedgwick, Morgan and Bent Counties. Be aware that your measurements were approximate and therefore may not match the ArcView areas exactly. Your area estimates should be within 50 - 100 square miles of ArcView's areas. Click the Zoom to extent of all themes button. Use the Identify tool to select and list the ArcView county data. Click the Identify tool on Sedgwick, Morgan, and Bent Counties. Notice how the information in the table changes as you select different counties. a) What are the ArcView areas displayed in the 'Identify Results' table for Sedgwick, Morgan, and Bent Counties? b) How do your results for Sedgwick, Morgan, and Bent Counties compare to the ArcView data? Close the 'Identify Results' table. Click on the in the upper left hand corner of the table and zoom out to full extent of the theme
Question 5	For the last question of Problem Set 1, you will convert the area of Bent County to acres. Use the ArcView data you recorded from the 'Identify Results' table. 1 square mile = 640 acres Convert area in square miles for Bent County to acres.
That's all for Problem Set 1	Click on the Unselect All button . With your teacher's permission you may exit Arcview. Click on File/Exit.