Area, Perimeter, Surface
Area and Volume Review
After this review you will be able to :
 Define area , perimeter, surface area and
volume
 Explain how to calculate area, perimeter,
surface area and volume
 Give real world situations when you would use
area, perimeter, surface area and volume
Area is the measurement inside an
object. It is the interior space.
How to Calculate the
Area of
Squares and Rectangles
To calculate the area of a square or rectangle all
you need to do is multiply the length times the
width of the figure.
2 in
Example: A=6x2=12 in ²
6 in
The answer is ALWAYS labeled in
units squared (u²).
5cm
5cm
Example: A=5x5=25 cm
²
Real World Uses of Area
You would need to calculate the area for:
 Figuring how much carpeting for the
floor area of a room
 How much wood for flooring in your
house
 The number of tiles to cover the
bathroom floor
Area of a Circle
For finding the area for circles, you need to square the
radius and multiply the answer times ∏ or 3.14
*Remember the radius is half of the (diameter) distance
across the center of a circle.
* Don’t get punked!
____6cm
A= r²x 3.14
A=6² x 3.14=113.04 cm²
*Notice the answer is in units squared!
Perimeter
The perimeter is the outside
measurement of a shape like a square
or a rectangle.
The outside of a circle is called the
CIRCUMFERENCE instead of the
perimeter, but it still measures the
outside of the shape.
How to Calculate the Perimeter
of a
Square or a Rectangle
To figure out the perimeter of a square or rectangle all
you have to do is add up all of the outside
measurements.
5 cm
5 cm
Example: P= 5+5+5+5=20cm
or
P=5x4=20cm
Example: P= 3+3+6+6=18 in
or
P= 2x3+ 2x6=18 in
3 in
6 in
Calculating Circumference
of
Circles

To determine the circumference you multiply the
diameter times ∏.

*Don’t get punked!!

Remember the diameter is the distance across the
center of the circle.
___12m___
 Example: C=d x 3.14
C=12 x 3.14
C=37.68 m
Real World Uses for Perimeter




Knowing how much fence you need to
put around your property
Buying enough wallpaper border to
make your bedroom look good
How much fabric to put a border
around a quilt you are making
Figuring how much lumber you need to
frame windows and doorways
Surface Area
Surface area is the total area of the
outside faces of three dimensional
objects
like cubes
prisms
and cylinders.
Calculating Surface Area


Since you already know how to determine the
area of two-dimensional shapes it will be easy
for you to figure out the surface area of 3-d
objects.
All you have to do is calculate the area of
each of the faces of cubes, prisms, or
cylinders and then total up all of your
measurements.
Calculating Surface Area
______10cm
So to calculate the surface area of this
cylinder you would first have to find out the
area of the two circles that make up the top
and base.
A = r²x ∏
A= 10² x 3.14
A = 314 cm²
* Don’t get punked!
There are two
circles so you have to double your area
answer. A = 314 cm² x 2 = 628 cm²
_____10cm
Calculating Surface Area

Now that you have the area of the two circles, you have
to figure out the area of:
the rectangle that is formed by the height of
the cylinder and the circumference of the circle
if you were to unwrap the cylinder. _
50 cm
g
l
u
e
h
e
r
e
_____10cm
Calculating Surface Area

First find the circumference of the circle:

*Don’t get punked by the radius!
C = d x 3.14
C = 20 x 3.14
C = 62.86 cm
The circumference is equal to the length of the
rectangle part of the cylinder net.
_
50cm
g
l
u
Length
e
h
e
of the cylinder
Calculating Surface Area
The next step in finding the surface area of
the cylinder is to calculate the area of the
rectangle now that you have figured out the
length by using the circumference of the
circle.
A=lxw
A = 62.8 x 50
A = 3140 cm²
The final step is to add the area of the two
circles from your first step.
____10 cm
SA= 628 + 3140 = 3768 cm²
50 cm
Real World Surface Area Situations




How much wrapping paper you need to wrap
your best friend’s birthday present
Figuring out how much paint you need to paint
each of the rooms of your house
It’s the number of square units needed to
cover the outside of a figure
How much siding or paint for the exterior of
your house
Volume

Volume is the measurement of the
interior capacity of a 3-dimensional
figure like a cylinder, cube, or prism.
How to Calculate Volume
•
When you calculate the volume of a 3-d object all you have to do is
use your prior knowledge of finding area.
•
Volume is just the area of the base times the height of the shape.
____30 ft____
•
The area of the base of this cylinder, as you know, is the
area of the circle or ∏ times the radius² so here is the next
step: *HINT: Don’t get punked by the diameter!!!
A=3.14 x r²
A=3.14 x 15²
A= 706.5 ft²
V=706.5 x 45
45 ft
V=31792.5 ft³
*NOTICE: VOLUME IS ALWAYS LABELED
UNITS CUBED! (u³)
Real World Volume Situations
Real world situations for needing volume include:

Calculating the capacity (how much) fuel a tanker
truck can carry

How much water could be stored in a water
buffalo…the tank, not the animal!

The available space in a silo to store feed corn or
grain for the winter

How much water you need to fill your swimming pool
for the summer