Lesson 10.9: Right Triangles and Regular Polygons
Review:
What are the three Trig. Ratios?
What is perimeter?
What is the formula for area of a triangle?
What is a regular polygon?
Regular Hexagon
Radius
a segment whose endpoints are the center
and a vertex
Center
the point that is equidistant from all vertices
Apothem
a segment that is a perpendicular bisector from the center to a side
Central Angle the angle between two radii
Regular Pentagon
360
Central Angle (CA)
# of angles/sides
Find the radius, apothem, and perimeter.
Regular Hexagon
Each side is 12 inches.
Find the apothem and perimeter.
Regular Octagon
Radius is 6 inches.
Area of a regular polygon.
Find the area of one triangle. Then multiply by the number of triangles.
OR
1/2 x apothem x perimeter
1ap
2
Find the area.
Regular Hexagon.
Perimeter is 108 cm.
Find the area.
Regular Decagon
Apothem is 20.
How many sides does a regular polygon have whose central angle is 15 degrees?
Will a central angle of 64 degrees create a regular polygon?
Given a regular 16­gon with a radius of 7 inches.
Find:
central angle
apothem
perimeter
area
Regular 50­gon
given: apothem is 9.5 cm
Find:
central angle
radius
perimeter
area