PART I

To help you write the area formula for any regular polygon, let us explore the area of a regular octagon.

1) Go toGeogebra.org/calculator. On the top of the page, select from the drop down menuGeometry. Press the MORElink on the left navigation panel to open additional geometric links. Draw a regular polygon using the Polygonslink on the left navigation panel. You can draw an octagon as the drawing below.

2) Using theBasic Toolsarea, select theSegmentlink, and draw all the diagonals of the polygon. 3) Label each congruent sides.Constructthe apothem segment of one of the triangles formed by the diagonal. Label the apothema.

4) Find the area of the little triangle using the software, and later write a generic equation for the area of the triangle. 5) Write the generic equation of the perimeter of the regular octagon.

6) Use all the information gathered above and write a formula for the area of the regular octagon. 7) Write a formula for the area of any regular polygon withnsides.