Geometry Section 10.3
Areas of Regular Polygons
Name:_______________________
Date:_____________ Period:_____
Target Goals:
1. To find the area of a regular polygon
What do we know so far….? Complete the following area formulas
1.) Area of Triangle =
2.) Area of a Parallelogram =
3.) Area of a Trapezoid =
4.) Area of a Kite/Rhombus =
Now let’s look at REGULAR POLYGONS
You can circumscribe a circle about any regular polygon. The center of the regular polygon is
the center of the circumscribed circle.
 The ____________ is the distance from the center to a
vertex.
 The ____________ is the perpendicular distance from
the center to a side.
Finding angle measurements
Discovering the area of a regular polygon:
Take a regular n-gon with side length s. The radii split the regular polygon into n congruent
isosceles triangles.
What is the area of each of the isosceles triangles?
How can you use the area of one of the triangles to find the
area of the regular polygon?
The area of a regular polygon is half the product of the ______________ and the
______________.
Practice, Practice, Practice:
Find the area of the regular polygons
1.)
2.)
3.)
Central angle:___
Triangle:
Central angle:___
Triangle:
Central angle:___
Triangle:
a:___
s:___
p:___
a:___
s:___
p:___
a:___
s:___
p:___
4.) Find the area of a regular decagon
with 12.3 in apothem and 8 in sides.
5.) Find area of a regular pentagon w/
11.6 cm sides and an 8 cm apothem
Central angle:___
Triangle:
Central angle:___
Triangle:
a:___
s:___
p:___
a:___
s:___
p:___
6.)
7.)
8.) Find the area of a regular
Hexagon with side length 4 in.
Central angle:___
Triangle:
Central angle:___
Triangle:
Central angle:___
Triangle:
a:___
s:___
p:___
a:___
s:___
p:___
a:___
s:___
p:___
9.)
10.)
11.) Find the area of a regular
triangle with apothem 5 m.
Central angle:___
Triangle:
Central angle:___
Triangle:
Central angle:___
Triangle:
a:___
s:___
p:___
a:___
s:___
p:___
a:___
s:___
p:___
12.)
13.)
14.) Find the area of a regular
square with radius 6 in.
Central angle:___
Triangle:
Central angle:___
Triangle:
Central angle:___
Triangle:
a:___
s:___
p:___
a:___
s:___
p:___
a:___
s:___
p:___