1. 11.3 Areas of Regular Polygons and Circles
Objectives: Find areas of regular polygons and circles.

2. apothem (of a polygon)
Apothem = line segment from center of polygon that is perpendicular bisector of a side of the polygon
Apothem = a a

3. area of a regular polygon
Regular polygon = all sides
are equal
Areareg polygon = ½ Pa,
P = perimeter of polygon
a = apothem a
12 in.

4. Find the area of a regular hexagon with a perimeter of 72 in.
Areareg polygon = ½ Pa,
P = perimeter of polygon
a = apothem
P = 72 in., a = ?
a = 63
A = ½ (72)(63 )
 in2 a

5. Find the area of a regular octagon with a perimeter of 80 in.
Areareg polygon = ½ Pa,
P = perimeter of polygon
a = apothem
P = 80 in., a = ?
Tan 22.5 = 5/a
a = 5 / tan =
A = ½ (80)(12.07 )
 in2
22.5° a
5 in.

6. Find the area of a regular triangle with apothem length of 30 in.
Areareg polygon = ½ Pa,
P = perimeter of polygon
a = apothem
P = 6x, a = 30 in.
tan 60 = x / 30
x = 30 tan 60 =
P =
A = ½ (311.77)(30 )
 in2
60° 30 x