Creative Maths brings you, maths made really clear with Dr Nic
Perimeter, area and volume - which is which and how to calculate them
Hi, I'm Dr Nic from Creative Maths and I love to help people learn maths and stats
Here are the aims for this video.
By the end you should be able to tell whether to calculate perimeter, area or volume in
a practical situation And give correct measurement units.
There are some practice examples for you near the end of the video
This video is about the concepts of perimeter, area and volume
with a little bit about finding the actual values.
We concentrate on rectangles and cuboids.
A rectangle is a four sided two dimensional shape with all angles right angles.
A square is a special kind of rectangle with all sides equal length.
Some people think a square is different from a rectangle,
but it is just a specific case of a rectangle.
A cuboid is a three dimensional object that has six rectangular faces.
It is also known as a rectangular prism.
A cube is a special kind of cuboid with all the faces being squares - like a die.
See in the description below for links to videos about other shapes.
First a quick overview of perimeter, area and volume
Perimeter is the distance around the boundary of a two dimensional or flat shape
Area is the amount of surface of a shape
Volume is the quantity of material in a three dimensional shape.
We use different units.
Perimeter is measured in a linear unit such as m, km, mm, inches, feet, miles
Area is measured in square units such as m2, km2, mm2, sq inches, sq feet (ft2), sq miles
Volume is measured in cubic units such as m3, km3, mm3, cubic inches, cubic feet (ft3), cubic miles
One way to think about it is that perimeter is string,
area is tiles and volume is clay.
I will now go through all of these individually.
If this is all very clear to you, fast forward to the section later with the questions.
Perimeter Perimeter is a specific name for the length
or distance around a shape.
The perimeter of this rectangle is fourteen units.
We can imagine a piece of string going around the shape to give us the perimeter.
To find the perimeter we add together the lengths of the sides.
The perimeter of this rectangle is 5 units plus 10 units plus 5 units plus 10 units,
which gives us 30 units.
Here are some examples of when we would want to calculate the perimeter of a shape
We would need to know the perimeter of a paddock to work out how long the fence will be.
When we run around a basketball court, the distance covered is the perimeter of the court.
If we were going to put a binding around the edge of a mat,
the perimeter would give us the amount of binding material needed.
Area Area is another name for surface.
We give area in numbers of squares or square units.
The area of this rectangle is ten squares.
We imagine square tiles covering the shape to give us the area.
To find the area of a rectangle, we multiply two length measurements that are at right angles.
This is sometimes called length times width
The area of this rectangle is 5 units times 10 units.
Even though there are four values shown,
we only multiply two numbers that are at right angles to each other.
Here are some examples of when we would want to calculate the area of a shape
We might need to know the area in order to decide how many tiles to cover a floor,
how much grass seed we need for a paddock
or the size of the evaporation surface of a pond.
Volume Volume is the quantity of material in a three dimensional shape.
The volume of this cuboid is 12 cubes.
We imagine how much clay we would need to make the solid object.
To find the volume of a cuboid, we multiply three length measurements that are all at
right angles to each other.
(This is called orthogonal) The volume of water in this (rather small)
swimming pool is 3 m by 5 m by 1.5 m which equals 22.5 m cubed.
Note that we have to be very careful that the three numbers we use to calculate with
are orthogonal or at right angles to each other.
Here are some examples of when we would want to calculate a volume of an object.
We want to know how much soil we need for a raised garden bed.
Or we want to know if the cake tin holds the right amount of cake mixture.
OR we need to know how much air there is in a room.
Another thing we might like to find is surface area
Solid three dimensional shapes also have area.
It is called surface area.
It is the number of squares needed to cover an object.
The surface area of this cuboid is 32 squares.
Imagine we are wanting to put square tiles all over the object (including underneath)
To find the surface area of a cuboid we find the area of each of the faces and add them
together.
It helps that the faces come in pairs.
In practical applications we usually only want the surface area of some of the faces.
The surface area of this swimming pool is (3 by 5 + 5 by 1.5 + 3 by 1.5) all times 2.
This gives 54 SQUARE metres (including the top).
Even though we are talking about a three dimensional object,
we are measuring the two dimensional surface AREA of it.
If we were thinking about tiling the inside of the pool
We would not want to include the top face in our calculations
The actual tiled area of the swimming pool would be 39 square metres.
(Not the top)
Here are some examples of needing to find the surface area of an object:
The amount of paint to paint a tank with.
The surface of a worm for moisture loss.
The amount of icing or frosting for a cake, bearing in mind we do not usually ice the bottom.
We have covered perimeter, area, volume and surface area.
Often the trickiest part is knowing which of them we need to calculate.
It is useful to know the names so that we can identify useful formulas."
Here are some applications.
For each one, pause and decide what needs to be calculated and what unit would be appropriate
before carrying on with the video.
Example 1: We need to know the amount of sand needed to cover an icy road.
Is this perimeter, area, volume or surfacearea?
Pause and think about it or discuss it.
We want to know the area of the road so that we can work out how much sand is needed.
It will usually be calculated in sq meters or sq yards.
Example 2: We are getting a quote for a fence around our swimming pool
Is this perimeter, area, volume or surface area?
Pause and think about it or discuss it.
We need to know the perimeter of the swimming pool surround,
which will give us the length of the fence.
The length will be in metres or feet.
Example 3 We are buying Christmas lights to go right round our house.
Is this perimeter, area, volume or surface area?
Pause and think about it or discuss it.
We need to know the perimeter of the house
which will give us the length of the string of lights.
The length will be in metres or feet.
Example 4 We need to know how much concrete is needed for a building slab.
Is this perimeter, area, volume or surface area?
Pause and think about it or discuss it.
We need to know the volume of concrete to fill in three dimensions.
The volume will be measured in cubic metres or cubic feet.
Example 5 We need to know if a paddock is big enough to feed seven sheep.
Is this perimeter, area, volume or surface area?
Pause and think about it or discuss it.
We need to know the area of the paddock The paddock will be measured in square metres
or square yards, which can be converted into hectares or acres.
Pasture fed sheep need about 500 square m per sheep.
Example 6 We are estimating the amount of paint we need to paint a shipping container
Is this perimeter, area, volume or surface area?
Pause and think about it or discuss it.
We need to know the surface area of the shipping container (but not the bottom).
It will usually be calculated in sq meters or sq feet.
Paint has a spreading rate that might be 10 sq metres per litre.
We use the spreading rate to work out how much paint we need for the calculated area.
So...How did you do?
If you have any questions ask in the comments below.
This video covered perimeter, area and volume of rectangles and cuboids
For more videos see in the description below.
Please like this video, subscribe, but most of all join the channel -
especially if you are using our videos in your teaching.
Help the channel grow and help me help more and more people like you.
I am truly grateful for my channel members who help make these videos possible.