Perimeter and Area
Please view this tutorial and answer the
follow-up questions on loose leaf to
turn in to your teacher.
Definitions
• Perimeter: The distance around the outside of
a plane shape
• Circumference: The distance around the
outside of a circle
• Area: The amount of space taken up by a
plane shape
Perimeter
When you are finding the
perimeter of a plane
shape, you must add up
the lengths of each side
of the shape.
12 ft
16 ft
16 ft
12 ft
Pick a starting point and then continue to work
your way around the shape until all sides have
been accounted for.
Perimeter
12 ft
I’ll choose the top left
corner as my starting
point.
16 ft
16 ft
12 ft
12 16 12 16  56
Perimeter
12 ft
So the perimeter of this
rectangle is 56 ft.
16 ft
16 ft
12 ft
12 16 12 16  56
Perimeter
The perimeter of a circle is called the
circumference.
To find the circumference of a circle, you can use
the following formulas:
C  2 r
or
C  d
Let’s take a look at an example.
Perimeter
C  2 r
5 ft
or
C  d
Do we have the radius or
the diameter?
5 is the radius so we can
use the first formula.
Perimeter
C  2 r
or
C  d
Let’s use 3.14 for pi
and 5 for the radius.
5 ft
C  2(3.14)(5)
C  31.4 ft
Area
The following is a list of formulas for basic plane
shapes:
1
Triangle: A  bh
2
Rectangle:
A  lw
Square:
A  bh
1
A  (b1  b2 )h
2
Parallelogram:
Trapezoid:
Circle:
A  r
2
As
2
Area
First, let’s try to find
the area of a triangle.
4 ft
6 ft
5 ft
1
A  bh
2
We can always tell
which values are the
base and height
because they will
always meet at a right
angle.
Area
First, let’s try to find
the area of a triangle.
4 ft
6 ft
5 ft
1
A  bh
2
In this case, 6 ft is the
base of the triangle and
4 ft is the height.
1
A  (6)(4)
2
2
A  12 ft
Area
Next up…a rectangle!
8 ft
10 ft
10 is the length and
8 is the width. Plug
these values into the
formula to find the
area.
A  lw
A  (10)(8)
A  80 ft
2
Area
You can use the same
formula to find the
area of a square.
4 ft
4 ft
A  lw
A  (4)(4)
A  16 ft
2
Area
Or you can use the
formula for a square.
You’ll get the same
answer for both.
4 ft
4 ft
As
2
A4
2
A  16 ft
2
A  lw
A  (4)(4)
A  16 ft
2
Area
Parallelograms are similar to rectangles, but you
have to be careful to choose the correct values
from the figure. You’ll need to find a base and
height.
5m
11 m
7m
Which values would
you choose for the
base and height?
Area
Since we know that base and height always
meet at a right angle, we should choose 11 for
our base and 5 for our height.
A  bh
5m
11 m
7m
A  (11)(5)
A  55m
2
Area
For a trapezoid, you’ll need to find two bases
and a height. Look for two sides that are parallel
and the length that connects them.
14 in
Which two sides are
parallel?
9 in
21 in
Area
The sides with lengths of 14 in. and 21 in. are
parallel. They are connected by a height of 9 in.
14 in
9 in
21 in
1
A  (b1  b2 )h
2
Plug these values
into the formula to
find the area of this
trapezoid.
Area
The sides with lengths of 14 in and 21 in are
parallel to each other. They are connected by a
height of 9 in.
14 in
9 in
21 in
1
A  (b1  b2 )h
2
1
A  (21  14)(9)
2
A  157.5in
2
Area
To find the area of a circle, you’ll need to find
the radius of that circle.
What is the value of
the radius in this
circle?
6 cm
Since 6 is the diameter,
we need to divide it by 2
to find the radius.
Area
To find the area of a circle, you’ll need to find
the radius of that circle.
So, the radius is 3.
6 cm
Plug this value into the
formula to find the area
for this circle.
Area
To find the area of a circle, you’ll need to find
the radius of that circle.
HINT: Use 3.14 for π.
A  r
2
A  3.14(3 )
2
6 cm
A  28.26cm
2
Follow-Up Questions
Answer the following questions on loose leaf
and hand them in to your teacher.
Follow-Up Questions
1) Find the perimeter of each figure.
a)
c)
17 m
13 cm
5 cm
23 m
12 cm
b)
9 ft
d)
8 in
4 ft
6 ft
4 ft
15 ft
Follow-Up Questions
2) Find the area of each figure.
a)
c)
14 m
12 cm
15 cm
14 m
18 cm
b)
11 in
9 ft
d)
4 ft
6 ft
4 ft
15 ft