# Area

## Learn that area is a measure of how much surface is covered. Explore the relationship between the size of the unit used and the resulting measurement. Find the area of irregular shapes by counting squares or subdividing the figure into sections. Learn how to approximate the area more accurately by using smaller and smaller units. Relate this counting approach to the standard area formulas for triangles, trapezoids, and parallelograms.

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### In This Session

Part A: Measuring Area
Part B: Exploring Area With a Geoboard
Part C: Scaling the Area
Homework

Area is a measure of how much surface is covered by a particular object or figure. Units of measure for area involve shapes that cover the plane, such as rectangles or squares. Common units in the U.S. customary system are square inches, square feet, square yards, and square miles; the standard unit in the metric system is the square meter.

For information on required and/or optional materials for this session, see Note 1.

### Learning Objectives

In this session, you will do the following:

• Learn that area is a measure of how much surface is covered and that some shapes cover the surface of a plane more completely than other shapes
• Examine how the size of the unit used to indicate the amount of surface covered determines the number of units
• Find the area of irregular shapes
• Learn how to approximate the area of shapes more accurately
• See how the process of counting can be shortened by using formulas
• Gain a deeper understanding of the standard formulas for the area of triangles, trapezoids, and parallelograms

### Key Terms

Previously Introduced

Scale Factor: A scale factor is a constant used to enlarge or reduce a figure. For example, if the sides of a triangle are enlarged to twice the length of the original triangle, we say the scale factor is 2.

New in This Session

Area: Area is a measure of how much surface is covered by a figure.

Midline: A midline is a segment connecting two midpoints of a triangle.

Similar Figures: Similar figures are figures that have the same shape but may be of different sizes. In similar figures, corresponding angles are congruent and corresponding segments are in proportion.

### Notes

Note 1

Materials Needed:

• Geoboard (optional)
• Rubber bands (optional)
• Power Polygons (optional)

Geoboards and Power Polygons can be purchased from:

ETA/Cuisenaire
500 Greenview Court
Vernon Hills, IL 60061
Phone: 800-445-5985/800-816-5050 (Customer service)
Fax: 800-875-9643/847-816-5066
http://www.etacuisenaire.com