http://www.ck12.org Chapter 10. Perimeter and Area
The area of each triangle isA 4 =^12 bh=^12 sa, wheresis the length of a side andais the apothem. If there arensides
in the regular polygon, then it is made up ofncongruent triangles.
Area of a Regular Polygon: If there arensides with lengthsin a regular polygon andais the apothem, then
A=^12 asnorA=^12 aP, wherePis the perimeter.
Example A
What is the perimeter of a regular octagon with 4 inch sides?
If each side is 4 inches and there are 8 sides, that means the perimeter is 8(4 in) = 32 inches.
Example B
The perimeter of a regular heptagon is 35 cm. What is the length of each side?
IfP=ns, then 35cm= 7 s. Therefore,s= 5 cm.
Example C
Find the length of the apothem in the regular octagon. Round your answer to the nearest hundredth.