Perimeter and Area of Polygons
Circumference and Area of Circles
Perimeter of Polygons
The perimeter of a polygon is the distance around the outside of the polygon.
- polygon is 2-dimensional
- perimeter is 1-dimensional and its measure in linear units as
feet (ft), yards (yd), meters (m), kilometers (km), etc.
Perimeter is used, for example ,
in determining how much fence is needed to put around of a garden plot,
or buying baseboard for a room.
In either case you will add up the lengths of the sides.
To find the perimeter of a polygon, P, take the sum of the lengths of its sides.
Area of Polygons
The area of a polygon is the amount of surface inside the polygon,
or the measure of the region bounded by the sides of the polygon.
-area is measured in square units such as
square feet (ft2), square yards (yd2), square meters (m2),
square kilometers (km2), etc.
Area is used, for example,
in buying carpet for a room,
or in determining how much paint you need if you want to paint a room.
To find the area of a polygon, A, means to find how many square units it takes
to caver the surface enclosed by the polygon.
Formulas
Triang le
P  a b c
c
a
h
A
1
bh
2
b
S q uare
Re c tang le
P  4s
P  2l  2 w
w
A  lw
l
s
A  s2
Formulas
Paralle lo g ram
P  2a  2b
h
a
A  bh
b
Trap e z o id
b
P  a b c B
a
c
h
A
B
1
h B  b
2
Circles
A circle is a set of all points in a plane equally distant from a fixed
point called the center of the circle.
Circ le
r
C
d
The radius (plural: radii), r, is a line segment from the center whose
endpoints both lie on the circle.
For the given circle, all radii have the same length.
The diameter, d, is line segment through center whose endpoints
both lie on the circle.
For the given circle, all diameters have the same length.
In any circle,the length of the diameter
is twice the length of the radius.
d  2r
d
r
2
Circumference and Area of Circles
The circumference, C, of a circle is the distance around the circle (its perimeter).
The ratio of the circumference of a circle to its diameter is
the same for all circles and is an irrational number called 
(the Greek letter pi, pronounced pie).

C
d
  31415926535897933238
.
...  314
.
The circumference, C, of a circle with diameter d and radius r is
The area, A, of a circle with radius r is
A  r 2
C  d
C  2r
Exercises
1. Find the perimeter and area of each polygon.
a)
b)
20 in
c)
8m
10 m
20 in
16 cm
10 m
8m
16 cm
20 m
P  4  20  80in
P  10  8  20  10  48m
6 8
6 8
A
 8 8
 112m2
2
2
A  20  20  400in 2
P  16  16  162  162  32  16 2cm  54.56cm
16  16
A
 128cm2
2
e)
d)
12.3 yd
4.2 yd
5 yd
20 m m
9.8 yd
P  5  12.3  9.8  27.1yd
9.8  4.2
A
 20.58 yd 2
2
6 mm
P  4  102  32  4 109cm  4176
. mm
3  10
A 4
 60mm2
2
Exercises
2. Square rug has perimeter of 30 in.
Find the dimension of each side of the rug.
P  4  a  30in
a  30  4  7.5in
a
a
3. A rectangular field is 75 meters wide and 100 meters long.
What is the area of the field ?
75
100
A  75  100  7500m2
Exercises
4. For each circle find circumference and area.
a)
b)
8m
30 m
C  30m  94.2m
C  2  8  16m  50.24m
A   8  64m  200.96m
2
c)
2
2
d)
60.9 km
12in
C  60.9km  19123
. km
C  2  12in  24in  7536
. in
2
2
 60.9 
2
2
2
2
 30 
. km A  12  144in  45216
. in 2
A      225m 2  706.5m 2 A    2   927.2km  291142
 2
5. Which is the larger and by how much: a pizza made in 16-in square
pizza pan or a pizza made in 16-in diameter circular pan?
square
A  16  16  256in 2
Square pizza is larger by
circle
 16 
A   
 2
256in 2  200.96in 2  554
. in 2 .
2
 64in 2  200.96in 2