Ex:cel Activity: From n-gons to circles

(1)Label columns of Excel Spreadsheet:

(2)In first column, put the numbers:

3, 4, 5, 6, 7, 8, 9, 10, 15, 20, 40, 50, 100, 150, 200, 300, 500, 1000, 5000, 10000, 100000

This would place the last number in the cell A22.

(3)In column B, we need to put the formula for calculating the sum of
the interior angles of a polygon. Do you remember it?______

(4)If you copy the formula you put in B2 and paste it in the cells B3 down to B22, it will automatically revise itself to fit each new row.

(5)In column C, we need to put the formula for calculating each interior angle of a regular polygon. The easiest way to do this would be to use the contents of columns A and B. What would this formula look like? ______

(6)Now for some trigonometry. For this table, we will assume that the radius of each polygon is 1: r = 1

Let us define x = the angle calculated in step 5.

Place an x in the figure at right to indicate where
this angle would be located for a pentagon.

Now write a trig proportion that relates the apothem and the radius (remember r = 1) using one of the trig functions.

______

(7)Solve the proportion written down in the previous step for the apothem a, and fill out column D using this formula. The instructor will have to show you a slight modification to your formula in order for it to give the correct results.

(8)Now write down another trigonometric proportion that relates the length of a side of the regular polygon to the angle x. There are several ways to do this.

______

Use this to find a formula to calculate the length of a side of a regular polygon. Put these formulas in column E.

(9)Now that you know the length of a side, use the contents of columns A through E to come up with a formula to automatically calculate the perimeter:______Put these formulas in column F.

(10)Use the formula for calculating the area of a regular polygon and the contents of columns A through F to automatically calculate the area of the regular polygon. Fill out column G with the appropriate formulas to calculate the area of each polygon.

QUESTIONS:

  1. A circle can be thought of as being like a regular polygon with an infinite number of sides. What would go in each of the following columns for a circle?

Column C:______Column D:______

Column F:______Column G:______

  1. What do you notice about the contents of columns C, D, F, and G as the number of sides increases?