Lesson Video: Perimeter: Unit Squares Mathematics • Third Year of Primary School

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.