area of regular polygons.notebook
April 13, 2015
4/13/15 - Warm Up Problem
Find the perimeter of each regular polygon.
7 ft
3 in
4 cm
P = ___
P = ___
P = ___
1
area of regular polygons.notebook
April 13, 2015
Concept 28 - Area of Regular Polygons
Goals
• identify the radius, apothem, and vertex angle of a regular polygon
• find perimeter and area of regular polygons
Regular Polygon: a polygon with congruent sides and congruent angles
Parts of a Regular Polygon
Center —point in the exact center of the polygon
Radius —segment drawn from the center to any vertex of the polygon
Apothem —segment drawn from the center to the middle of any side
Vertex Angle —the angle between a radius and an apothem ­ its vertex is the center Vertex Angle =
180
# of sides
2
area of regular polygons.notebook
April 13, 2015
Draw a radius and an apothem in each polygon.
What is the measure of the vertex angle?
3
area of regular polygons.notebook
April 13, 2015
Area of a Regular Polygon
Area = ½ * Perimeter * apothem
A = ½ Pa
To find the area of a regular polygon Find each of the following values:
vertex angle = _____
a (apothem) = _____
8
b (base) = _____
s (side) = _____
7
8
P (Perimeter) = _____
A (Area) = _____
4
area of regular polygons.notebook
April 13, 2015
You are working in a landscape/garden center this summer. One day, customer comes in wanting to know how much it will cost to tile the floor of an outdoor gazebo in her yard. Tile is $1.50 per square foot.
If each side of the gazebo is 5 ft and the distance across the gazebo is 8 feet, how much tile is needed and how much will tiling the floor cost?
8 ft
5 ft
5
area of regular polygons.notebook
April 13, 2015
Assignment:
Concept 28 Worksheet #1
(front side only)
vertex angle = _____
a = _____
3.5
b = _____
s = _____
3
3.5
P = _____
A = _____
6