Polygons

Polygons

Area of an Octagon

Opening

Area of an Octagon

How can you find the area of this octagon?

Math Mission

Opening

Find the area of regular polygons.

Find the Area of Regular Polygons

Work Time

Find the Area of Regular Polygons

All of these figures are regular polygons. In each figure, a vertical line has been drawn from the center of the figure to the midpoint of a side. This line is called the apothem. Note that the center of a regular polygon is the same distance from the midpoint of any side. Choose one of these figures, then:

  • Use the length of the apothem and the side length to find the area of the polygon. (To get started, think about how you could divide the polygon into shapes that you know how to find the area of.)
  • If you have time, find the area of a second polygon.

Hint:

  • How could you divide the polygon into triangles?
  • How could you divide the polygon into parallelograms?
  • How could you use the triangles to make a parallelogram that represents the total area of the polygon?

Find the Area of Regular Polygons

Work Time

Find the Area of Regular Polygons

Look at this floor plan of a build-it-yourself log cabin. Assume the cabin is a regular polygon.

  • What is the area of the cabin?

Prepare a Presentation

Work Time

Prepare a Presentation

Prepare a presentation about finding the area of regular polygons. Support your thinking with your work.

 

Challenge Problem

If the area of a regular hexagon is 64.5 square inches, and the apothem is 4.3 inches, how long is each side?

Make Connections

Performance Task

Ways of Thinking: Make Connections

Take notes about other students’ approaches to finding the area of regular polygons.

Hint:

As your classmates present, ask questions such as:

  • How is the apothem like the radius of a circle?
  • How was your approach to finding the area of the pentagon different from your approach to finding the areas of the other polygons? How was it the same?
  • What did you do first when solving the cabin problem—that is, how did you make sense of the problem?

Area of Regular Polygons

Formative Assessment

Summary of the Math: Area of Regular Polygons

Write a summary about finding the area of regular polygons.

Hint:

Check your summary.

  • Do you explain how to find the area of a regular polygon in at least two ways?
  • Do you explain how a regular polygon is different from a polygon that is not regular, in a way that makes it easier to find its area?

Reflect On Your Work

Work Time

Reflection

Write a reflection about the ideas discussed in class today. Use the sentence starter below if you find it to be helpful.

Some places I see regular polygons are …