Chapter 17: Activities 321
5. Press r. Notice that although the three graphs defined by Y5 are different, they share the
same derivative.
N = 4 sides
N = 8 sides
N = 12 sides
Computing Areas of Regular N-Sided Polygons
Problem
Use the equation solver to store a formula for the area of a regular N-sided polygon, and then
solve for each variable, given the other variables. Explore the fact that the limiting case is the area
of a circle, pr
2
.
Consider the formula A = NB
2
sin(pàN) cos(pàN) for the area of a regular polygon with N sides of
equal length and B distance from the center to a vertex.
Procedure
1. Press t B to select B:Solver from the MATH menu. Either the equation editor or the
interactive solver editor is displayed. If the interactive solver editor is displayed, press
} to
display the equation editor.
2. Enter the formula as 0=ANNB
2
sin(p / N)cos(p / N), and then press Í. The interactive solver
editor is displayed.
3. Enter N=4 and B=6 to find the area (A) of a square with a distance (B) from center to vertex of
6 centimeters.
4. Press } } to move the cursor onto A, and then press ă \. The solution for A is
displayed on the interactive solver editor.
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