Areas of Regular Polygons
Objective: To find the areas of
regular polygons
Mrs. McConaughy
Geometry
1
Definition: Regular Polygon
an equilateral and
Regular polygon-___________________
_______________________________________
equiangular polygon
Mrs. McConaughy
Geometry
2
KEY
areas of
AreaFinding
∆ = ____________
irregular polygonal regions:
 Divide the irregular region into
familiar geometric regions.
 Determine individual areas.
 Add to determine total area.
Mrs. McConaughy
Geometry
3
Divide
Divide the
polygon
into isosceles
the
polygon
on the∆s.LEFT
 Find the area of each triangle.
into
familiar
geometric
regions.
 Add to determine the total area.
height (apothem)
Base (side)
NOTE: Each region is an isosceles ∆.
Mrs. McConaughy
Geometry
4
Area ∆ = ½ bh
Regular Polygon Area Theorem
= ½ sa
Area (reg. poly.) = The
½ as
n*,ofwhere
n ispolygon
the is
area
a regular
number of sides.
Mrs. McConaughy
given by the formula
__________________,
where
A = ½ asn
A is the Area, a is the
apothem, s is the length of a
side, and n is the number of
sides of the regular polygon.
Since the length of each side
times the number of sides (sn)
is the perimeter
_______________,
the formula can also be written
A = ½ ap
____________.
Geometry
5
Decisions, Decisions, Decisions…
NOTE: When a problem gives you (or
asks you to find the perimeter of a
regular polygon, use ______________.
A (reg. poly.) = 1/2 ap
NOTE: When a problem gives you (or
asks you to find the length of a side of
a regular polygon, use _____________.
A (reg. poly.) = 1/2 asn
Mrs. McConaughy
Geometry
6
Determine which area formula to
use. Explain (underline KEY
words).
1. Pentagon; a ≈ 3 cm and s ≈ 4.4 cm
A = __________
2. Decagon; a ≈ 9.7 cm and s ≈ 14.1 cm
A = __________
3. Octagon; a ≈ 12.1 cm and p ≈ 80 cm
A = __________
4. Nonagon; p ≈ 63 cm and a ≈ 9.6 cm
A = __________
Mrs. McConaughy
Geometry
7
Determine which area formula to use.
Explain (underline KEY words).
5)
Find the area of a regular polygon with a ≈ 12 cm
and p ≈ 81.6 cm.
A = __________
6) Find the perimeter of a regular polygon to the
nearest tenth of a meter if a a ≈ m and A ≈
259.2m2.
A = __________
7) Find the length of each side of a regular polygon to
the nearest foot if a ≈ 80 ft., n = 20, and A ≈
20,000 square feet.
A = __________
Mrs. McConaughy
Geometry
8
Final Checks for Understanding
•
•
•
Use your new theorem to find the area of a
regular polygon accurate to the nearest
square centimeter.
Find the area of a regular heptagon if the
apothem is 3.2m in length and the length of a
side is 4m.
Find the perimeter of a regular polygon if the
apothem is 7cm in length and the area =
182cm2.
Mrs. McConaughy
Geometry
9
Homework Assignment:
Areas of Regular Polygons WS
Mrs. McConaughy
Geometry
10