what is the formula for the area of a regular polygon?

A =(1/4) n a^2 ctn (180/n)

A is area
a is length of side
n is number of sides
ctn is cotangent

if the angle of a regular polygon is 20 degrees how many sides does the ploygon have? 18 sides, but show your work

The formula for the area of a regular polygon depends on the number of sides (n) and the length of each side (s). The formula is:

Area = (n * s^2) / (4 * tan(pi/n))

Where:
- n is the number of sides of the polygon.
- s is the length of each side.
- pi is a mathematical constant approximately equal to 3.14159.
- tan() represents the tangent function.

The formula for the area of a regular polygon depends on the number of sides it has. To find the area, you need to know the length of the sides and the apothem (the distance from the center of the polygon to the midpoint of any side).

For a regular polygon with n sides and side length s, and apothem a, you can use the following formula to find the area (A):

A = 0.5 * n * s * a

To calculate the area of a regular polygon, you need to know the number of sides, the length of the sides, and the apothem length. The apothem can be found by using trigonometry or other methods, depending on the given information.

For example, if you have a regular hexagon with a side length of 6 cm and the apothem length is unknown, you would need to find the apothem before calculating the area.