Now, repeat the process for additional regular polygons. In the dynamic geometry sketch, you can also change the number of sides of the figure by clicking on "more" to add more sides to the regular polygon, or "less" to reduce the number of sides in the regular polygon.

Use the sketch to generate several different regular octagons. Record the radius and apothem of 5 of these regular octagons in a table like the one shown. You may create the table in your notes.

Once you have recorded the values for the radius and apothem, calculate the value of the cosine of 180 degrees divided by the number of sides 180° number of sides , where the number of sides is the number of sides in the regular polygon (in this case, a regular octagon). Use that value to fill in the middle column of the table.

How do the values in the middle column compare to the values of the apothem given to you by the sketch?

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Check Your Answer

The values in the middle column, radius × cos (180 degrees over number of sides 180° number of sides ) are equal to the length of the apothem.