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?