# math

The apothem of a regular polygon is the distance from the center to any side.
If the length of the apothem remains constant at 10 inches, the formula for the perimeter of a regular polygon as a function of the number of sides is ( ) ( )( ).
As the regular polygon changes from a pentagon (5 sides) to an octagon (8 sides), what is the approximate average rate of change in the perimeter?

1. 👍 0
2. 👎 0
3. 👁 416
1. If the perimeter is p, the area is A = 1/2 ap.

So, since p = ns, what is the side s of an n-gon?

The central angle of each of the n isosceles triangles is θ=360/n, so the side is

s = 20 tan(θ/2)

Thus, the area is

A = 1/2 a (ns) = 1/2 (10) (n*20 tan 180/n)
= 100n tan(180/n)

You can probably handle the rest, eh?

1. 👍 0
2. 👎 0
posted by Steve

## Similar Questions

1. ### algebra

The apothem of a regular polygon is the distance from the center of the polygon to a side. Explain how to derive a formula for the area of a regular polygon using the apothem.

asked by lucy on February 10, 2012
2. ### algebra

the apothem of a regular polygon is the distance from the center of the polygon to a side. Explaiin how to derive a formula for the area of a regular polygon using the apothem.

asked by lucy needs help now on February 12, 2012
3. ### Math--Area

Find the area of each regular polygon to the nearest tenth. Octagon with side length of 10 kilometers. Heres what I tried; but I don't know if im on the right track. Area=1/2 * Perimeter* Apothem Perimeter=base of octagon* number

asked by natalie on April 4, 2007
4. ### College Geometry

In this assignment, you examine a process that links polygons and circles. You will reach some quantitative conclusions about their respective areas and the relationship between the two. As you know, a regular polygon has sides of

asked by Lisa on September 3, 2013
5. ### Geometry

the side of a regular hexagon is twice the square root of its apothem. find the apothem and side length.

asked by Sofia on January 12, 2011
6. ### Th

the area of a regular polygon varies jointly as its apothem and its perimeter. express the area in terms pf apothem a and the perimeter p

asked by Mary on August 28, 2014
7. ### math

The exterior angle of a regular polygon is the angle formed by an extended side and the adjacent side. c) How do the central angel and the exterior angle of a regular pentagon compare? Is this relationship true in any regular

asked by CAITLIN D. on May 17, 2009
8. ### math

A side of regular polygon is 3.5 cm in length.the perimeter of the polygon is 17.5 cm. How many sides does the polygon have?

asked by nimshi on September 30, 2012
9. ### geometry

in a regular polygon, with center O, and a side AB, measure of angle AOB =72 degrees. If AB is 4.6 in. find the perimeter

asked by mark on April 10, 2011
10. ### Math/Geometry

Can you help me with this? Find the area of each regular polygon. Round to the nearest tenth. 1. an equilateral triangle with an apothem 8.9 inches long

asked by Stan on March 3, 2010

More Similar Questions