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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
12 ft
16 ft
Pick a starting point and then continue to work your way around the shape until all sides have
been accounted for.
Perimeter
I’ll choose the top left corner as my starting
point.
12 ft
16 ft
12 ft
16 ft
1212 +1612 +16 +1212 +16 +12 +1612 +16 +12 +16 =56
Perimeter
So the perimeter of this rectangle is 56 ft.
12 ft
16 ft
12 ft
16 ft
1212 +1612 +16 +1212 +16 +12 +1612 +16 +12 +16 =56
PerimeterThe perimeter of a circle is called the
circumference.
To find the circumference of a circle, you can use the following formulas:
C =2πr C =πdor
Let’s take a look at an example.
Perimeter
5 ft
C =2πr C =πdor
5 is the radius so we can use the first formula.
Do we have the radius or the diameter?
Perimeter
5 ft
C =2πr C =πdor
Let’s use 3.14 for pi and 5 for the radius.
C =2(3.14)(5)C =31.4 ft
Triangle: Circle:
Rectangle: Square:
Parallelogram:
Trapezoid:
AreaThe following is a list of formulas for basic plane
shapes:
A =lw
A =bh
A =s2
A =πr2A =
12bh
A =12(b1 +b2 )h
Area
5 ft
First, let’s try to find the area of a triangle.
6 ft
4 ft
A =12bh
We can always tell which values are the
base and height because they will
always meet at a right angle.
Area
5 ft
First, let’s try to find the area of a triangle.
6 ft
4 ft
A =12bh
In this case, 6 ft is the base of the triangle and
4 ft is the height.
A =12(6)(4)
A =12 ft2
Area
8 ft
Next up…a rectangle!
10 ft
10 is the length and 8 is the width. Plug
these values into the formula to find the
area.
A=80 ft2
A =lwA =(10)(8)
Area
4 ft
You can use the same formula to find the area of a square.
4 ft A=16 ft2
A =lwA =(4)(4)
Area
4 ft
Or you can use the formula for a square.
4 ft A =16 ft2
A =lwA =(4)(4)
A =s2
A =42
A=16 ft2You’ll get the same
answer for both.
Area
11 m
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.
7 m
Which values would you choose for the base and height?
5 m
Area
11 m
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.
7 m5 m
A =bh
A =(11)(5)
A =55m2
Area
21 in
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
9 inWhich two sides are
parallel?
Area
21 in
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 Plug these values into the formula to find the area of this
trapezoid.
A =12(b1 +b2 )h
Area
21 in
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
A =12(b1 +b2 )h
A =12(21+14)(9)
A =157.5in2
AreaTo find the area of a circle, you’ll need to find
the radius of that circle.
6 cm
What is the value of the radius in this
circle?
Since 6 is the diameter, we need to divide it by 2
to find the radius.
AreaTo find the area of a circle, you’ll need to find
the radius of that circle.
6 cm
So, the radius is 3.
Plug this value into the formula to find the area
for this circle.
AreaTo find the area of a circle, you’ll need to find
the radius of that circle.
6 cm
HINT: Use 3.14 for π.
A=πr2
A =3.14(32 )
A =28.26cm2
Follow-Up Questions
Answer the following questions on loose leafand hand them in to your teacher.
Follow-Up Questions
17 m
23 m
1) Find the perimeter of each figure.
a)
b)
8 in
c)
5 cm
12 cm
13 cm
d) 9 ft
15 ft
6 ft4 ft 4 ft
Follow-Up Questions
14 m
14 m
2) Find the area of each figure.
a)
b)11 in
c)
18 cm
12 cm15 cm
d) 9 ft
15 ft
6 ft4 ft 4 ft
