Investigating Mathematics with GeoGebra

Henrico County Public Schools

How do you find the area of a regular polygon?

READ the instructions on the right and INTERACT with the GeoGebra applet below.

Sorry, the GeoGebra Applet could not be started. Please install Java 1.4 (or later) to use this page.
Sorry, the GeoGebra Applet could not be started. Please install Java 1.4 (or later) to use this page.

Investigation Steps

Click on the reset icon icon to reset the diagram.

 Figure 1 Close 
  1. Move the green point on the slider.
    What relationship exists between the triangles and the hexagon?

  2. How can the given information be used to determine the area of a regular hexagon?

  3. Can you develop a formula using the perimeter of a regular hexagon and it’s apothem to determine it’s area?

  4. Move either blue point to change the size of the hexagon.
    Explain how the area of a regular hexagon is a function of it’s dimensions.

 Figure 2 Close 
  1. Move the green point on the slider.
    What relationship exists between the triangles and the octagon?

  2. What is the area of this regular octagon?
    Can you develop a formula using the perimeter of a regular hexagon and it’s apothem to determine it’s area?

  3. Move either blue point to change the size of the hexagon.
    How do you find the area of regular polygon with n sides?
    Can you explain your reasoning?