Areas of Regular Polygons
Day 2
Geometry
Central Angle of a Regular Polygon
A central angle of a regular polygon is an angle
whose vertex is the center.
You can divide 360 by the number of sides to
find the measure of each central angle of the
polygon.
Find the Central Angle
Find the Central Angle
When would we need to know the
central angle?
• Finding the side length
of the regular polygon
• Finding the apothem of
the regular polygon
REGULAR QUADRILATERAL
SQUARE
REGULAR HEXAGON
Examples
Examples
1. Find the area of a regular hexagon with each
side 5.
2. Find the area of a regular hexagon with a
radius of 8.
What about other regular
polygons?
Other Regular Polygons
We will have to use trig to find the missing sides of
other regular polygons.
1. Find the central angle
2. Draw in the apothem to make a right triangle
3. Divide the central angle by 2 to get the angle in the
right triangle
4. Set up a trig function to find the missing sides.
Find the area of the
Regular Pentagon
Find the area of the regular octagon
Find the Area of a Regular Dodecagon
The enclosure on the floor underneath the
Foucault Pendulum at Houston Museum of
Natural Sciences in Houston, Texas, is a regular
dodecagon with a side length of about 4.3 feet
and a radius of about 8.3 feet. What is the
floor area of the enclosure?
Example
The bottom of a glass is a regular 12-gon with
a side length of about 1.2 cm and a radius of
2.3 cm. What is the area of the bottom of the
glass?