### Video Transcript

Perimeter: Unit Squares

In this video, we’re going to learn
how to count unit squares to find the perimeter of rectilinear shapes that’ve been
drawn on unit grids.

This is Ethel. She loves gardening. In fact, one of the areas of her
garden that Ethel’s most proud of is where she grows her carrots. The only problem is last time she
planted some carrots, most of them ended up looking a little bit like this. She had some fairy visitors who ate
most of them before they grew. And so this year, Ethel’s decided
to be prepared. She wants to buy a wooden fence to
go all the way around her carrot plot.

Now what can we say about Ethel’s
fence? Well, firstly, we know that it
needs to go all the way around the area where she’s going to plant her carrots. There can’t be any gaps at all. Secondly, we can say that the
length of the fence that Ethel needs is the same as the distance around the plot of
land. In maths, we use the word perimeter
to describe this. The perimeter of a shape is the
distance around it. Finally, because this shape has
been drawn on squared paper for us, we can measure the perimeter of the shape by
counting the length of the squares. We could call the length of a
square one unit.

So how many units should Ethel’s
fence be? And where do you think we should
start measuring from? Well, it doesn’t matter where we
start measuring a perimeter of a shape from as long as we stop when we get back to
the beginning. And to help us remember to stop, it
probably makes sense to start in one of the corners or vertices. Let’s start measuring from this
vertex here. Why don’t you trace the perimeter
with your fingers as we count? One, two, three, four, five, six,
seven, eight, nine, 10, 11, 12, 13, 14, 15, 16, 17, 18. And we’re back where we
started. The perimeter of the shape is 18
units. And so Ethel is going to need to
buy a fence that is 18 units long.

This is Rob. He loves eating carrots, but today
he fancies a cabbage. But unfortunately, he can see that
some person who just doesn’t care much about where poor rabbits like him are going
to get their lunch has put a perimeter fence all the way around. I wonder who that could be. Now, from where Rob is sitting, the
fence looks like it goes all the way around. But imagine there was a gap. Then he’d be able to find his way
into the cabbages. Best thing to do is if Rob runs all
the way around the outside; then he’ll know for sure. Now, in this picture, we can see
that the length of each square is worth one meter in real life. Remember that when we measure the
perimeter of a shape, we don’t count the squares themselves. We count the lengths of each
square. Now Rob could start from wherever
he wants, as long as he stops when he gets back to the beginning.

Let’s measure each side and add as
we go along. Two square lengths plus three
equals five plus another three equals eight. The length of the top of our shape
is nine squares long. And if we add this to eight, our
total becomes 17. 17 plus five equals 22. And the last side of this shape is
six squares long and 22 plus six equals 28. The perimeter of this shape is 28
square lengths. And because on this diagram the
length of a square is worth one meter, the perimeter of the shape that Rob is going
to have to run around in real life is 28 meters. Remember, the perimeter is simply
the distance all around it.

Let’s try answering some questions
now where we have to put into practice what we’ve learned. We’re going to need to find the
perimeter of some shapes by counting the units or the lengths of each square all the
way around the outside.

Find the perimeter of the shaded
region.

Part of the square grid that we can
see has been shaded in. And it makes this interesting
shape. This is the shaded region that the
question talks about. And in the question, we’re asked to
find the measurement of this region. We’re not asked to find the length
or the width or the height. We’re asked to find this shape’s
perimeter. What does the word perimeter
mean? A shape’s perimeter is the distance
all around it. So if we’re going to find the
perimeter of this shape, we’re going to need to decide where to start and then count
how many units or square lengths it takes to go all the way around back to where we
started. We can’t leave any gaps. It must be the complete
distance.

To make sure we remember where we
started, it makes sense to start from one of the vertices or corners of the
shape. Let’s start measuring from this
vertex here. Let’s count each unit together,
one, two, three, four, five, six, seven, eight, nine, 10, 11, 12, 13, 14, 15, 16,
17, 18. And we’re back where we
started. We know that the perimeter of a
shape is the distance all around it. And we found the distance all
around this shape by starting in a corner and counting all the unit lengths that go
all the way around. The perimeter of the shaded region
is 18 units.

In the figure below, determine the
perimeter of the shaded part, given that the side length of every small square is a
unit.

In the picture or the figure that
we’re given, we can see a shaded shape, and it’s been drawn onto a square grid. And we’re told something about this
grid. We’re told the side length of every
small square is one unit. And so whatever measuring we need
to do in this question, we can do the measuring in units. Now we’re asked to determine or to
work out the perimeter of the shaded part. Now, what is a shape’s
perimeter? Perhaps you’ve heard people talking
about the perimeter fence around a field or the white lines that make up the
perimeter of a sports pitch.

If you’ve heard perimeter used like
this, then you’ll know that the word has got something to do with the outside of a
shape. Perimeter is the word we use to
describe the distance all around a shape. And so if we want to find the
perimeter of the shaded part that we can see here, we’re going to need to find the
distance all around it. Let’s start from this corner
here. Remember, we can’t stop until we
get back where we started. One, two, three, four, five, six,
seven, eight, nine, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20. And then the longest side, 21, 22,
23, 24, 25, 26, 27, 28. The distance all around this shape
is 28 square lengths. And because we’re told that the
side length of every small square is a unit, we can say that the perimeter of this
shaded part is 28 units.

The given diagram shows the floor
plan of David’s house. Which of the shaded rectangular
rooms has the greatest perimeter?

This picture or diagram shows the
floor plan of David’s house. It’s like a map of all the
different rooms. Are we’re looking down on it to see
the different shapes. In this question, we’re looking in
particular at the shaded rectangular rooms. So we’re thinking about Matthew’s
bedroom, David’s bedroom, and also the kitchen over here. And we’re asked which one of these
has the greatest perimeter. Now we know that the perimeter of a
shape is the distance all around it. So we could actually read the
question like this, which of the shaded rectangular rooms has the greatest distance
around it?

Now imagine for a moment that we’re
standing in each of these rooms one by one. We wouldn’t be thinking about the
size of the room in the way that we’d normally look at a room and think, that’s a
big room. If we were trying to do this in
real life, we’d probably have a tape measure of some sort and we’d be measuring the
distance all around the room. Just because our room looks big
doesn’t necessarily mean it’s got the largest perimeter. Well, we don’t need to use a tape
measure to find the answer; we’re not standing in the rooms. We’ve got a floor plan to help. And so what we’re going to have to
do is to count the lengths of the squares that go all the way around. We could call these squares
units.

Let’s start by measuring the
perimeter of the kitchen. The longest side here is six units
long, and this shorter side is two units long. Then we’ve got another long side of
six and another shorter side of two. This is interesting, isn’t it? We’ve got two lots of six and two
lots of two. This shows us what we know about
rectangles, doesn’t it? They have two pairs of equal
sides. We know that six plus two equals
eight. And if we had another lot of six
plus two or another lot of eight, we get a total of 16 units altogether. The distance all around the kitchen
is 16 units.

Now let’s measure the perimeter of
Matthew’s bedroom. This side here is three squares
long. Then this longer side is four
squares long. Then just like before, we have
another lot of three and another lot of four. We know that three plus four equals
seven. And so if we had another lot of
three plus four or another lot of seven, we get double seven, which is 14. The distance all around Matthew’s
bedroom is 14 units.

Now let’s measure the perimeter of
David’s bedroom. This side here is four units
long. This longest side along the top is
six units long. We know that four and six make 10,
don’t we? Can you guess what the whole
perimeter is going to be? We have another side of four and
another side of six. As we’ve said already, four plus
six equals 10. And if we add another lot of four
plus six or another lot of 10, we get double 10, which is 20.

By counting the square lengths or
the units all the way around these shaded rectangular rooms, we found which room has
the largest perimeter. The perimeter of the kitchen is 16
units. The perimeter of Matthew’s bedroom
is 14 units. But the perimeter of David’s
bedroom is 20 units. Out of the three shaded rectangular
rooms, the one that has the greatest perimeter is David’s bedroom.

So what have we learned in this
video? We have learned that the perimeter
of a shape is the distance around it. We’ve also learned how to find a
perimeter of shapes drawn on a grid by counting unit squares.