Areas of Regular Polygons
Geometry
Unit 4, Lesson 3
Regular Polygons
• Regular Polygon is any Polygon that is both equiangular and equilateral.
• You can circumscribe a circle about any regular polygon.
Regular Polygons (cont.)
• The center of a regular polygon is the center of the circumscribed circle.
Center
Regular Polygons (cont.)
• The radius of a regular polygon is the distance from the center to a vertex
CenterRadius
Regular Polygons (cont.)
• The apothem of a regular polygon is the perpendicular distance from the center to a side
CenterRadius
Apothem
Theorem 5-9:Area of a Regular Polygon
• The area of a regular polygon is half the product of the apothem and the perimeter.
• A = ½ap
a
p
Example:
• Find the area of a regular decagon with a 12.3 in apothem and 8 in sides?– First: What is the number of sides?– Second: Find the perimeter.– Third: Plug into the formula
• Answer: 492 in2
Example:
• Find the area of a regular pentagon with the sides of 11.6 cm and apothem of 8 cm
• Area = ½ (8cm) (11.6 x 5) =232 cm2