Posted by **Anonymous** on Thursday, May 24, 2012 at 10:22pm.

area of a nonagon with a perimeter of 126in

- math -
**MathMate**, Friday, May 25, 2012 at 7:38am
The area A of any regular polygon of n sides with side length s, apothem a is

A=nas/2.

Since ns=perimeter, p, we can also write the area as

A=ap/2

An apothem is the distance from the centre of the polygon to the side.

We assume the given nonagon is regular, i.e. all sides and interior angles are equal.

A nonagon has 9 sides. Each side is of length 126/9=14". We need first to find the apothem as follows.

The central angle for each side is 360/9=40°.

Each side of the nonagon forms an isosceles triangle with the centre of the nonagon. Its half vertical angle equals 40/2=20°.

The height of this triangle is the apothem and can be calculated by the trigonometric formula

a=(s/2)/tan(20)=7cot(20)

Using the formula above:

Area = ap/2=126*7cot(20)=882cot(20°)

## Answer this Question

## Related Questions

- Geometry - Find the area of a nonagon with a perimeter of 126 inches. Round to ...
- math - one of the two numbers that can be both the perimeter and the area of the...
- Math - There's a triangle the numbers on each sides are 22 25 and 11 What is it'...
- 2nd grade math - If you have a rectangle with 24 square units 3 lines down 8 ...
- Math - find the sum of the interior angles of a nonagon. I know a nonagon has 9 ...
- 3 rd grade Math - how are perimeter and area? When building your club house did ...
- math (area&perimeter) - the demensions of a rectangle are 5y for the height, and...
- math/geometry - the area of one triangle is 9dm^2 and its perimeter is 4x-4. The...
- math - Find the dimensions of a rectangle with perimeter 40 with the largest ...
- Math - Perimeter of rectangle = 2*l+b. Area = l*b. If l = 1m, b = 55cm. Find ...