Solve for a for the area of a regular polygon.

Expert Answers

An illustration of the letter 'A' in a speech bubbles

The general formula for the area of a regular polygon is:


where the apothem is a line segment between the center and one of its sides and the perimeter is the sum of the lengths of all sides.

For a regular polygon, the apothem=`s/(2tan(180/n))`

This can be verified for an equilateral triangle (regular 3 sided polygon) where the general formula for area is:

The apothem is equal to ```s/(2tan60)=s/(2sqrt3)`

And the area is =`((3s)(s))/(2sqrt3)=(sqrt3s^2)/2`

For a square, the apothem is `s/2` and the perimeter is `4s`, therefore


For a pentagon, the apothem is = `s/(2tan36)=0.688s`

And the area is=`((0.688s)(5s))/2=1.72s^2`

See eNotes Ad-Free

Start your 48-hour free trial to get access to more than 30,000 additional guides and more than 350,000 Homework Help questions answered by our experts.

Get 48 Hours Free Access
Approved by eNotes Editorial