Lesson video

Hello, my name is Dr.

Rolanson, and I'm excited to be guiding you through today's lesson.

Let's get started.

Welcome to today's lesson from the unit of perimeter, area, and volume.

This lesson is called Checking Understanding of Perimeter.

And by end of today's lesson, we'll be able to find the perimeter of many different polygons or compound shapes.

Here are some previous keywords that you may be familiar with, and I'll be using again in today's lesson.

So pause the video while you remind yourselves about the meanings of these words and then press Play when you're ready to continue.

This lesson contains three learn cycles.

In the first learn cycle, we'll be focusing on understanding what perimeter is and what it means.

In the second learn cycle, we'll be looking for efficient methods to calculate perimeters for different shapes.

And the third learn cycle, we'll be given the perimeters and we'll go try and find missing lengths using that information.

But let's start off with learn cycle one, understanding perimeter.

Now, perimeter is a length that wraps around a 2D space.

So for example, if you imagine a context where this rectangle represents a field that is surrounded by a wall.

In this context, which could be found by calculating the perimeter of the field? Is it the total amount of grass or is it the total length of the wall? Pause the video while you think about this and press Play when you're ready to continue.

In this context, the perimeter of the field is the total length of the wall.

If you almost imagine breaking this wall off and lining them all up to make one long wall, we could look at how long that wall would be.

So for example, if I took that 90 there, and then we'll have 120, then we'll have another 90, then we'll have another 120, if we have that as one long wall, it would be 420 metres.

But the reality is that wall wraps around the field to make its perimeter.

So the perimeter is 420 metres.

So the perimeter is the distance around a 2D shape.

And because it's a length, perimeter can be measured using any units of length, for example, centimetres or inches.

I wonder if you can think of any other units of length that could be used to find the perimeter.

Pause the video while you think about this and press Play when you're ready to continue.

Other units of length include millimetres, metres, and kilometres, or any other metric unit of length will be work well as well.

And units of length could also be feet, yards, and miles if working with imperial.

So perimeter can be found by summing the lengths of the sides of a shape.

Here we have two pupils who have calculated or tried to calculate the perimeter of that rectangle.

Who has correctly calculated the perimeter of the rectangle, is it Jun or is it Sophia? Pause the video while you think about this and press Play when you're ready to continue.

So trying to decide this, we should really think about why the calculations are different.

Jun is only adding together two numbers, eight and five, while Sophia is adding together four numbers, eight, five, eight, and five.

So why are they different? Well, Jun has only added together the two lengths that you can see the numbers for.

But there are four sides to that shape.

So Jun has not included all the sides when calculating the perimeter, whereas Sophia has thought about, well, those other two sides that don't have numbers on.

Because it's a rectangle, those measurements must be the same as the sides that she can see.

So the top side must be five and the right-hand side must be eight.

So Sophia's done eight and five, add eight, add five.

She has added together all four sides in that rectangle, so that one is the correct perimeter.

So here we have another example, and we've got Alex and Sam who have both tried to calculate the perimeter of the triangle.

Who's done it correctly this time? Pause the video while you think about this and press Play when you're ready to continue.

So once again, let's think about why the calculations might be different.

Alex has added together three numbers: eight, five, and six.

Whereas, Sam has added together four numbers: eight, five, and six, and also another four.

Well, with Alex's working, the eight, five, and six are all sides on that triangle, whereas with Sam's working, we've also got the four as well.

Now, that four isn't one of the sides of the triangle, it's the height of the triangle.

But if you imagine wrapping a fence around that triangular field, for example, that four wouldn't be one of the fences there.

So it does actually add to the perimeter, it is just the height of it.

So that means Alex's working is correct work, because Sam has included a length that is not on one of the sides.

So let's check what we've learned so far.

Which of these units could be used to measure perimeter? Is it A, kilogrammes, B, kilometres, C, litres, or D, square centimetres? Pause the video while you have a go at this and press Play when you're ready for an answer.

The answer is B, kilometres.

Here's another question.

The rectangle below is made of square tiles.

What is the perimeter of this rectangle? Is it A, 2 metres B, 6 metres, C, 8 metres, or D, 12 metres? Pause the video while you have a go and press Play when you're ready for an answer.

The answer is D, 12 metres.

Which shape has a perimeter of 16 centimetres? Is it A, B, or C? Pause the video while you have a go and press Play when you're ready for an answer.

The answer is C, because we've got five plus three, plus another five, plus another three.

If you put B, I understand why you put that, 'cause it is 10 plus 6 is 16.

But it's not B, because you've got a third side of that triangle there which hasn't got a measurement on it, but that would make it more than 16 centimetres.

And if you put A, I understand why even that as well, because you've done 6 plus 3 plus 5 plus 2, which gives 16.

But remember, that 2 is not one of the sides of the triangle so it doesn't contribute to the perimeter.

So the answer is C.

Okay, it's over to you now for task A.

This task consists of two questions.

In question one, you define the perimeter of each of these shapes.

Pause the video while you have a go and press Play when you're ready for question two.

And here is question two.

Take the triangles that contain enough information to calculate the perimeter, by summing together the given lengths.

All the lengths of these diagrams are given in centimetres.

Pause the video while you have a go and press Play when you're ready for some answers.

Okay, well done, let's go through some answers.

Here's question one.

In 1A, we have a perimeter of 12 metres, that's 4 plus 3 plus 5.

In B, we have 16 metres, which is 5 plus 3 plus 5 plus 3.

And in C, it's 18 centimetres, which you can either do by doing 4 plus 5 plus 4 plus 5, or you could just count the edges of those squares around the outside instead.

And in question two, the triangles that contain enough information to calculate the perimeter by summing together the given lengths are B and D.

Those are ones we are given the lengths of all three of those sides.

Great work so far, now let's move on to the second learn cycle, which is finding efficient methods to calculate the perimeter.

So Aisha's found the perimeter of this shape here.

And she says, "I started at the top of the shape and summed each of the lengths in order." So we start at the top, we can see we've got a two.

And then if we go, say, clockwise round, we'd have five and then four and three.

So Aisha's done it 2 plus 5 plus 4 plus 3 plus 3 plus 4 plus 5 plus 2, to get 28.

'Cause it's metres, the units are metres.

But then surely, there must be a more efficient method here.

Is there a more efficient way of doing this? Pause the video while you think what you might do differently and press play when you're ready to continue.

So Jacob has found the perimeter of the shape in a different way.

He says, "Each length appears twice, so I double each length before summing them." So we can see each length of appears twice, if we just look at the shape from the top down to the bottom, we can see we have two twos at the top, and then we have two fives, and then we've got two fours towards the bottom, and then two threes underneath.

So if I'm gonna add all those together, we could do it by doing 2 times 2 and then 2 times 5 and 2 times 4 and 2 times 3, and adding all those together to get 4 plus 10 plus 8 plus 6, which is 28 metres.

Is there a more efficient way than that? Well, Izzy has found the perimeter of the shape in a different way again.

She says, "The lengths are all the same on each side, so I summed at the lengths on the left and then multiplied it by two." So if we look at the diagram again, we can see we've got the two and the five and the four and the three on the left-hand side.

On the right-hand side, we'd have another two, five, four, and three.

So Izzy has added together 2, 5, 4 and 3, and then she's timed it by 2, so she's done 2 times 14 to get 28 metres.

So the perimeter for shapes with symmetry or repeating patterns can be calculated using different methods.

We've got Aisha's method, we've got Jacob's method, and we've got Izzy's method.

Out of those three methods, whose method seemed the most efficient? Pause the video while you think about this, maybe discuss it with someone else if you can, and press Play when you're ready to continue.

Now, that might be down to personal opinion slightly, but what we can definitely see here is how using multiplication can speed up the process of finding perimeter, in cases where there are repeated additions within the shape, usually 'cause there's patterns or symmetry in some sort of way.

We can also see that Izzy's method requires less writing down than the other methods because she's only adding together those four numbers, then she's timesing it by two, whereas the other two methods have a lot more operations involved in them.

So here's another example.

A shape is formed by reflecting the four line segments over two mirror lines.

Now, you can see that we've got the four line segments which have three, two, four, and one as their lengths, and those lengths are given in centimetres.

And the mirror lines are represented by the dashed grey lines we have on the screen there.

So we create the shape like this.

Find the perimeter of this shape.

Pause the video while you have a go at this and think about what might be the most efficient method for doing this, and then press Play when you're ready to continue.

Okay, let's do this together now.

We could start off this by adding together the four lengths that we know, three plus two plus four plus one.

And then because we can see that there are four lots of those lengths on this shape, we can take our answer and then multiply it by four.

So to get 4 times 10, which gives us 40.

And because it's centimetres, our units are centimetres.

Here we have another example.

We've got a Pentagon, because it has five sides, and we can see that all the sides have these little markings on them.

It says, "Sides which have the same markings have equal lengths." Therefore, find the perimeter of this shape.

Now, there's a couple of different ways we can do this.

But we can definitely acknowledge that if that bottom length there is 10 millimetres, all of the other lengths must be 10 millimetres as well.

So method one could be to write on all those 10 millimetres and think to ourselves, right, we need to add them together.

So we'll do 10 plus 10 plus 10 plus 10 plus 10, to get 50 millimetres.

Or method two could be thinking, well I know that bottom one's 10, I know I've got 5 lots of those, so I could do 5 times 10 to get 50 millimetres.

Which of those methods seems most efficient to you? Pause the video while you think about this, maybe discuss it with someone else, and press Play when you're ready to continue.

Okay, let's check what we've learned there, then.

Find the perimeter of this shape.

We have an octagon, it's eight sides, and all the sides have those markings on.

Pause the video while you have a go at this and press play when you're ready for an answer.

So the answer is eight lots of 10, eight times 10 is 80 centimetres.

Here's another question.

The dashed line represents a mirror line here.

What is the perimeter of this shape? Is it A, 19 centimetres, B, 38 centimetres or C, 40 centimetres? Pause the video while you have a go and press Play when you're ready for an answer.

The answer is B, 38 centimetres.

If you put A, I think you've just added together the sides you can see there.

But don't forget, there are more sides on the other side of that mirror line as well, which are the same.

So you can add those together and times it by 2 to get 38.

If you've put 40, I think you may be thinking about trying to find how long it is in between.

You don't really know how long it is in between, but it also doesn't contribute to the perimeter either.

Let's now look at another situation.

Andeep starts with a rectangle, with all lengths in centimetres.

He cuts a rectangle out of the corner of that rectangle to make a composite rectilinear shape.

How does doing this affect the perimeter of the shape? Pause the video while you think about this, maybe think, has the perimeter got bigger, has it got smaller, is it the same? And press Play when you're ready to continue.

Now, there are some unknown lengths on this composite shape, but the unknown vertical lengths on it sum to the total height of the shape.

We can see if we work from the bottom upwards, we see we've got B, which goes vertical upwards.

Then where that stops, then we've got A going vertical upwards as well.

If we put that A and B together, we can see that A plus B must add up to 10.

Now, we don't know what A and B are, but we do know that together, those two sides add up to 10.

And then, the same with the horizontal ones as well.

If we look at the horizontal length, D and horizontal length, C, we don't know what either of those are individually, but if we work from left to right, we first have D.

And then where D stops, that's kind of where C starts and then goes over to the other end of the shape.

So if we put those together, D plus C, or C plus D, they must equal eight.

Now again, we don't know how big C or D is individually, but we do know that they sum to eight.

So these two shapes actually have equal perimeters.

Both of them have a perimeter of two lots of 10 plus eight, which is 36 centimetres.

So let's use that idea now to find the perimeter of this shape.

We've got a composite shape, with lots of sides we don't know the lengths of.

But I think we can still find the perimeter.

Pause the video while you think about this and then press play when you're ready to work through it together.

Now, we can see that that vertical length on the right-hand side is 13 centimetres, and we have four other vertical lengths on this shape.

None of them overlap over each other in any kind of way and they're not joined by any diagonals.

One vertical length stops, the next one starts.

So those four vertical lengths must sum to 13 centimetres.

You imagine pushing them all together like this, they would add up to 13.

And then we can see we've got 10 centimetres running across the horizontal side, on the base.

There are four other horizontal lengths on the shape.

And again, because they do not overlap in any kind of way, they're not joined by any diagonals, those four horizontal lengths must also sum to 10 centimetres.

Therefore, the total perimeter is 2 lots of 13 plus 10, which makes 46 centimetres.

So let's think about this, then.

On the left-hand side, we have a rectangle which is overlaid over a grid.

And the perimeter of that rectangle is 18 units.

And on the right-hand side, we have a composite shape also overlaid over a grid.

Are the perimeters of these two shapes equal? Just pause the video while you think about this and press play when you're ready to continue.

Yes, the perimeters of these two shapes are equal.

The perimeter on this L shape is also 18 units because the shorter lengths in each direction sum to the longest length in the same direction.

So how about this one? Do these two shapes have equal perimeters? Pause the video or have a think and press Play when you're ready to continue.

The answer is no, the perimeter is not 18 units because one of the lengths in this case is diagonal.

You look at where that diagonal length is, it goes diagonally from one corner of a square to the other.

Now, that distance is shorter than if you'd gone vertically downwards and then horizontally across instead.

So the perimeter actually will be less than 18 in this situation because you've got that diagonal length.

How about on this one? Are the perimeters of these two shapes equal? Pause the video while you have a think and press Play when you're ready to continue.

Now, this one doesn't have any diagonal lengths, but no, they are not equal.

That's because the perimeter is not 18, because some of the vertical lengths overlap with each other.

We can see on the vertical lengths, we've got four on the left-hand side and then we've got two in the middle, and then there's another one in the middle there before you got the three on the right-hand side.

Now, that two on the one, they overlap with each other.

It's like you're going back on yourself a little bit.

Now, if you add those, the three on the right hand side, you'd get more than the four what's on the left-hand side.

And you'd get more than what the length is of the rectangle on the left-hand side of the slide.

So the perimeter of this one is not 18 because some of those vertical lengths overlap with each other.

So let's check what we've learned there.

Here we have a composite shape, a composite rectilinear shape, 'cause it's made out of lots of rectangles and we're to fill in the blanks.

We've got A plus B plus C equals? Pause the video while you work that out and press Play when you're ready to continue.

The answer is 50.

Those four vertical lengths must all add up to the 50 centimetres on the right-hand side of that shape.

Which shape has the same perimeter as this rectangle? Is it A, B, or C? Pause the video while you think about this and press Play when you're ready for an answer.

The answer is C.

In shape A, we've got some of those vertical lengths overlap with each other, so the perimeter will not be the same as the rectangle.

And in B, we can see we've got a diagonal length in there too, so that perimeter will not be the same as the rectangle either.

Whereas with shape C, if you imagine pushing those horizontal lengths together at the top and those vertical lengths together on the left-hand side, you'd have the rectangle that is above it.

And so they would have the same perimeter.

Okay, over to you now for task B, this task contains three questions, and here is question one and two.

Question one, these shapes were formed by reflecting line segments over the dashed mirror lines, find the perimeter of each shape.

And in question two, you've got three shapes that all have markings on the sides of the shape and you need to find the perimeter of each shape.

Pause the video while you work through these and press Play when you're ready for question three.

And here is question three.

Find the perimeter of each composite rectilinear shape, all lengths are given in metres.

Pause the video while you have a go at these and press Play when you're ready to go through the answers.

Great job with that, let's now go through some answers.

In question one, in A, the perimeter is 16 metres.

In B, it's 48 centimetres.

And in question 2 we can do this with multiplication by doing 3 times 12 and 4 times 5 and 6 times 11, and we would get 36 metres, 20 centimetres, and 66 millimetres.

And in question three, we wanna find the perimeters of these.

We'd get a perimeter of 40 metres for question A and also 40 metres for question B.

You're doing great.

Now let's move on to the third and final learn cycle of this lesson, which is find the missing lengths when the perimeter is known.

The perimeter of this shape is 18 centimetres.

Find the missing length.

So we can see we've got eight and four and A.

Now, those three must add together to make 18.

So we've got 12 plus A makes 18.

We can work that out by doing 18, subtract 12 to get 6.

So the missing length must be six centimetres.

Here's another example.

The perimeter of this shape is 18 centimetres, find the missing length.

Now, this time there are no numbers visible on the shape, but what we do see is that there are markings on each of those sides, which means all 3 of those sides must be the same length and all 3 of them add up to 18.

So if that bottom length is A, all the sides must be equal to A.

So we've got A plus A plus A is 18, which means 3A is 18, 3 times A is 18.

So you can work out the value of A by dividing both sides by three, and we get A equals six centimetres.

And here's another example.

The perimeter of this shape is 18 centimetres, find the missing length.

Now, here we can see we've got one of the lengths is given to us, which is four centimetres and we've got A across the bottom.

We don't know the other two lengths, but we do, don't we? Because they've got markings on them, which means the vertical length on the right-hand side must be four centimetres, and the horizontal length at the top must be equal to A.

So we've got A plus 4 plus A plus 4 gives you 18, which means we've got 2A plus 8 gives you 18, so 2A must be equal to 10, and 1A must be equal to 5.

So the missing length is five centimetres.

Okay, let's check what we've learned.

The perimeter of each shape here is 20 metres.

In which shapes could the missing length be four metres? Now, it could be more than one.

So you got choice of A, B, and C.

Pause the video while you have a go at this and press Play when you're ready for answers.

The answers are A and C.

In A, if we do seven plus nine plus four as the missing length, we'd get 20 metres altogether.

And C, if we did four multiplied by five, 'cause there's 5 lots of that 4 we'd get 20 metres.

If you put B, you might be thinking about doing 8 plus 8 to get 16, subtracting that 16 from the 20 and that leaves you with 4.

But remember, there are two sides which are equal to B there, you would have to share that four between those two sides, the top and bottom.

So actually, the value B there is two.

Okay, it's over to you now for task C.

This task contains one question.

Here it is.

The perimeter of each shape is 24 metres.

Find the value of each of the unknowns.

Pause the video while you have a go at this and press Play when you're ready to go through the answers.

All right, well done.

And let's now go through some answers together.

In part A, we could do 7 plus 4 plus 7 and then subtract it from 24 to get 6.

In part B, we could divide 24 by 6, and that would give us 4.

In part C, we could add together 9 with another 9 and then subtract that from 24 to get 6.

In part D, we could subtract the 10 from 24 first, which means it must be 14 leftover for the other 2 sides in that triangle.

Both of those sides are equal to D.

So 14 divided by 2 is 7.

In part E, that five metres has nothing to do with the perimeter, so we could ignore that.

We could add 8 with another 8 for its parallel side and then subtract that from 24, which will leave us with 8 left, then divide that by 2 for the top and bottom side of that parallelogram, and that'll give us 4.

Now in F, we can see that the vertical sides, we've got five on the left and those other two vertical sides must add up to five as well.

So we've got 10 that are going vertically.

And going horizontally, we've got six we can see.

And then on that bottom side, some of that is six metres, and there's just a little bit left over, and that's the same as the F at the top.

So we could take the 6 and the 6, add those together, add them to the 10 we had earlier, subtract it from 24 and then divide it by 2 for the the F at the top and a little bit of F that's left over on the base as well.

And we'll do that and we'll get one for the value of F.

Oof, how do you get on with that? Great work today.

Here's a summary of what we've learned in this lesson.

The perimeter is the distance around a 2D shape.

And the perimeter of any polygon or compound shape made of polygons can be found by summing together the lengths of the sides.

And some methods of finding perimeters are more efficient than others, especially when there's repeating patterns or a symmetry in some sort of way.

And when we know the perimeter, it can sometimes enable us to find missing lengths in a shape as well.

Great work.