11.6 Area of Regular Polygons
EQ: How do we find the area of a
regular polygon?
Vocabulary
In the diagram, ABCDE is a regular
pentagon inscribed in F.
𝐁𝐅 and 𝐀𝐅 are radii.
𝐆𝐅 is the apothem. It is the shortest
distance from the center to a side of a
regular polygon.
The central angle is formed by 2 radii. To
find it, divide 360 ̊ by the number of
sides.
EQ: How do we find the area of a regular polygon?
Area of a Regular Polygon
𝐴=
1
𝑎𝑃
2
or 𝐴 =
1
𝑎𝑛𝑠
2
𝑎 = apothem
𝑃 = perimeter
𝑛 = number of sides
𝑠 = side length
EQ: How do we find the area of a regular polygon?
Find angle measures in a regular polygon
EXAMPLE 1
In the diagram, ABCDE is a regular
pentagon inscribed in F. Find each
angle measure.
a.
m
AFB
EQ: How do we find the area of a regular polygon?
Find angle measures in a regular polygon
EXAMPLE 1
In the diagram, ABCDE is a regular
pentagon inscribed in F. Find each
angle measure.
b.
m
AFG
EQ: How do we find the area of a regular polygon?
Find angle measures in a regular polygon
EXAMPLE 1
In the diagram, ABCDE is a regular
pentagon inscribed in F. Find each
angle measure.
c.
m
GAF
EQ: How do we find the area of a regular polygon?
EXAMPLE 2
Find the area of a regular polygon
You are decorating the top of a table by
covering it with small ceramic tiles. The table
top is a regular octagon with 15 inch sides and
a radius of about 19.6 inches. What is the area
you are covering?
EQ: How do we find the area of a regular polygon?
Find
EXAMPLE
EXAMPLE 22
Findthe
thearea
areaofofaaregular
regularpolygon
polygon
EXAMPLE
2
EXAMPLE 2
EQ: How do we find the area of a regular polygon?
EXAMPLE 3 Find the area of a regular polygon
A regular nonagon is inscribed in a circle with
radius 4 units. Find the area of the nonagon.
EQ: How do we find the area of a regular polygon?
EXAMPLE 4
Find the area of the regular polygon.
EQ: How do we find the area of a regular polygon?
EXAMPLE 5
Find the area of the regular polygon.
EQ: How do we find the area of a regular polygon?
Summary
EQ: How do we find the area of a regular polygon?
We will use ________ functions or the ___________ Theorem to calculate
the _____________ and __________. Then we will plug it into the formula
𝑨=
𝟏
𝒂𝑷
𝟐
𝟏
or 𝑨 = 𝒂𝒏𝒔 where
𝟐
𝑎 = ________
𝑃 = ________
𝑛 = ________
𝑠 = ________