Section 11.6 ~ Areas of Regular Polygons
Topics in this lesson:
• center of a polygon
• radius of a polygon
• apothem of a polygon
• central angle of a polygon
• area of a regular polygon
Objective: To be able to find the area of
any regular polygon.
Vocabulary
center of a polygon ­ the center of its circumscribed circle
radius of a polygon ­ the radius of its circumscribed circle
apothem of a polygon ­ the distance from the center to any side of the polygon central angle of a regular polygon ­ an angle formed by two radii drawn to consecutive vertices of the polygon
Example 1
ABCDEF is a regular hexagon inscribed in G. Find each angle measure.
DEF
*Because ΔEGF is isosceles, GH is a perpendicular bisector.
Area of a Regular Polygon
The area of a regular n­gon with side length s is half the product of the apothem (a) and the perimeter (P).
A = Example 2
A wooden coaster is a regular octagon with 3 centimeter sides and a radius of about 3.92 centimeters. What is the area of the coaster?
Example 3
A regular nonagon is inscribed in a circle with radius 5 units. Find the perimeter P and area A of the nonagon.
.
Example 4
What is the area of a regular 24­gon with a side length of 10 inches?
Example 5
What is the area of a regular 30­gon with a radius of 20 feet?