Lesson video

Hi, welcome to our lesson on securing understanding of perimeter and area.

By the end of this lesson, you'll be able to find the perimeter in the area of basic shapes.

Now this is recapping work that you've done in your primary school, so you may find that some of this is quite familiar.

Of course you might find that some of it you do know, but perhaps you've forgotten.

So this lesson will help you with that.

We're going to start by reviewing some of our keywords.

On the screen right now you can see three of them.

What I'd like you to do in a moment is pause the video and have a go at writing down what you think the definitions are of each word and then we'll check them.

Pause the video now.

Welcome back.

Let's have a look at those keywords.

As you can see, a parallelogram is a type of quadrilateral with two pairs of parallel and equal sides.

Now you may have something similar to that, but do check that your definition meets the same criteria as ours.

It's not enough to say a parallelogram is a quadrilateral because there are lots of quadrilaterals such as rectangles, squares, kites, we don't wanna get confused.

Now comes to the two major keywords for today's lesson.

The first is perimeter.

Perimeter is the distance around a 2D shape and area is the size of the surface and states the number of unit squares needed to completely cover that surface.

Some people like to think of perimeter, I.

e.

the rim, helping us that it means the outside, and area as the space inside the shape.

So if that's something similar to what you've written down, well done.

You've got the right understanding.

Now you're ready for our lesson today.

This is our outline for our lesson.

We're going to start with the first section which is calculating the perimeter and area of rectangles.

The perimeter is the distance around a 2D shape.

Let's have a look at this rectangle.

We can see it has a length of 10 units and it has a width of three units.

To find the total distance around the shape, the side lengths are summed.

The perimeter is therefore three plus 10, so that's our length plus our width that we can see in our diagram.

But we mustn't forget that there's a second width and a second length.

And because this is a rectangle, we know that second length and that second width must be the same as the ones we can see.

So in other words, we have two lots of three and two lots of 10.

Now we've written it out here without writing two lots of because we want to be clear that there are four lengths in total and there are four values.

Once we get more practise of course we wouldn't necessarily write all of these out but it's absolutely fine to do so.

Our total perimeter is therefore 26 units.

Remember, we know the lengths that are not marked because this is a rectangle and because it's a rectangle, we know that the properties mean that the length and its opposite are the same and the width and the opposite side are the same.

Now the area is shown by the solid colour inside the rectangle.

The area is found by calculating the number of unit squares needed to completely cover the solid purple colour.

Here you can see I've put on a square grid for you.

Now at this point I'd like you to pause the video and just write down what you think the length and the width of this rectangle are.

Pause it now.

Welcome back.

Let's see how you got on.

We have a length of 10 and a width of three.

Now you could have put 10 squares and three squares if you like, but because I don't know the length of one of those little squares, I've written the word units.

Now in order to find this area, I could count all of the squares, but it is more efficient to multiply.

If you'd like, you can pause a video now to count the squares.

The alternative of course is that you could multiply.

We can see that we have three rows, each of 10 squares, so that's three lots of 10.

In other words, our area is 30 square units.

Now a quick check to see how you're getting on.

The area of a rectangle is found by adding the four side lengths.

Is this true or is this false? And whichever one you pick, you need to justify your answer.

So either select A or B to go with your true or false.

Pause the video now and make your selection.

Welcome back.

Let's see how you got on.

Exactly, it's false.

Area is the size of the space inside a 2D shape.

What was the name again for the distance around our 2D shape? That's right, perimeter.

So if we want to add the four side lengths together, we want to calculate perimeter and that's not what our question asked.

Our question asked about area.

It's now time for your first task.

In this, you can see there are three different rectangles shown on the screen.

Jun wants to work out the area in the perimeter of each of these rectangles.

Which rectangles have enough, too much, or not enough information? So for each one, write down if you have enough information to work out the area and work out the perimeter.

If you have too much information so there's more than than you need, or if there's not enough to work out the area and perimeter.

It may be that you have enough for one and not the other.

It's up to you to decide.

Pause the video now while you have a go.

It's now time for part B.

We will come to the answer to part A, so don't worry.

But let's carry on with our task.

I'd now like you to find the area and the perimeter of the rectangles where you do have enough information.

So find the area and perimeter of the rectangles where possible.

Pause the video now and have a go.

Welcome back, time for the final part of our task.

Jun works out the area of Z using the calculation 40 multiplied by 40 multiplied by 40 multiplied by 40.

What have they done wrong? Pause the video while you write down your answer.

Welcome back.

Let's go through our answers.

In question A, we asked which rectangles have enough, too much, or not enough information.

Well for X, we simply don't have enough information.

We've got a length there, but we don't have the length of the shorter side and without that we can't calculate area 'cause we multiply length by width and we can't find the perimeter either.

For Y, we have exactly the right amount of information.

We know one of the lengths and we know one of the widths or we could say one of the longer sides and one of the shorter sides.

And therefore for area, we are set.

For the perimeter, we need to work out the other two sides but we can do that using the properties of rectangles.

In Z, we have too much information, we didn't need to know all of that.

We only need to know the length of a longer side and a shorter side.

And in fact, we can see that because of the measurements used, Z's in fact a square.

So if they told me that Z was a square, I only needed to see one of those lengths and then I could have worked everything out.

Let's move on and look at B.

In here we asked you to find the area and perimeter where it was possible.

Now that means for X we don't have anything because it wasn't possible to find the area and perimeter because our shorter length is missing.

But for Y we can.

The perimeter for Y will be 25 add 25 add six add six because we have two longer sides of the same length and two shorter sides of the same length.

So when we sum that, we get a total of 62 and you'll notice that I've got a unit of measurement there.

There's an M for metres because that was the unit used in the question.

So it's important I write that same unit in my answer.

For the area, I just need to multiply the longer side and shorter side together.

So 25 times six giving me 150 metres squared.

Now let's look at C.

We wanted to find the area and perimeter of this shape.

Well the perimeter is where we sum the four sides, so that's 40 add 40 add 40 add 40.

Or you could have written four lots of 40, which gives us a total of 160 millimetres.

The area is where we multiply, so 40 times 40 giving us 1,600 millimetres squared.

Now in part C, Jun's had a go at working at the area and has done the calculation 40 times 40 times 40 times 40.

What did they do wrong? That's right, they multiplied every length together instead of multiplying the length by the width.

It sounds like Jun got a little confused about perimeter where we're summing all the sides and area where we're multiplying.

It's now time to move on and look at the second part of our lesson.

In this, we are thinking about rectangles perhaps a little more deeply than we have before, and in this section we're gonna be thinking about the same perimeter, does it mean the same area? Let's have a look.

A rectangle has a perimeter of 40 units.

Is this enough information to be able to draw the rectangle? What do you think? All of these shapes are rectangles.

Pause the video and have a quick go at calculating the perimeter of each of them.

That's right, the perimeter for every single one is 40.

But I think it's quite clear, we can see their areas look very different.

In particular we can see that some of them are quite compact, some of them are more stretched.

But even if I start trying to rearrange them and fit them together, I think it's clear that they're not gonna take up the same amount of space.

What's interesting though is the length and width pair you can see there.

What do you notice about it? Pause the video and write down what you notice.

So what did you notice? Well done if you spotted that the pair that you can see when added together give a total of 20.

In other words, the length plus the width is equal to half of the perimeter.

Maybe that's a fact I can use to solve more problems. A rectangle has a perimeter of 180 units.

Which of these cannot be the dimensions of my rectangle? Pause the video while you work this out.

Welcome back.

Which one did you pick? If you picked C, you've chosen correctly.

Remember we just talked about the length added to the width is half of the perimeter.

In other words, these length and width pairs should sum to make 90 because 90 is half of the perimeter.

Well in A, 45 add 45 is 90, so that's fine.

B, 30 add 60 is 90, so that's fine too.

In C though, 90 plus 90 is 180.

There's no way that rectangle can be our rectangle because the length plus the width cannot equal the whole perimeter.

But just to make sure, we'll check D too, 25.

2 add 64.

8, yep, that's also 90.

So the one that cannot be true must be C.

When the perimeter and the area of a rectangular are known, it is possible to calculate the dimensions of our rectangle.

Remember when we just had the perimeter, there were lots of different rectangles we could have had.

With perimeter and area though it becomes just one rectangle we are describing.

Let's look at this one.

A rectangle with an area of 20 square units has a perimeter of 18 units.

How do we work out the dimensions? Well when we're solving problems, it can be really handy to draw a diagram.

So let's draw one so that we can visualise what it is we are being asked about.

So I've drawn a rectangle with an unknown length and an unknown width.

I know that when I add the length and the width together, it's equal to half the perimeter.

So the length plus the width must be equal to nine.

I know when I multiply the length and the width together I'll get the area of my rectangle.

So that means the length multiplied by the width is 20.

What pair of numbers multiply therefore to make 20 but add to make nine? Pause the video while you work this out.

Welcome back.

Did you solve it? If you did, you'll know that you should have chosen the numbers five and four.

It's up to you which way around you want to put them but since we think of length as the longer side I'd say that one's five and the width would've been four.

Now knowing the perimeter and area of the rectangle can help you to visualise what that rectangle looks like.

A rectangle has a perimeter of 16 metres and an area of 16 metres squared.

Which of these images could represent this rectangle? Pause the video and have a go.

Welcome back.

Did you use the same reasoning we used earlier? Remember, the length plus the width must sum to make half of the perimeter.

So in other words, our length and our width added together will make eight.

When we multiply these numbers, they'll make 16.

So what pair of numbers add to make eight but multiply to make 16? Did you work out that it would be four and four? So I'm looking for a rectangle with a length of four and a width of four.

Well, there's no way that's gonna be A, it's quite clear that length and width are not the same.

In C, they look like they're the same but if you remember our previous lesson when we were checking our understanding of perimeter and area, we did talk about the fact we can't assume that lengths are the same unless we're told.

And C does not have the notation we require.

Therefore, the only shape here that actually is a square is B.

Well done if you chose that one.

Now it's time for our second task.

In this one we're going to be using our knowledge of what shapes look like based on their area and perimeter.

So let's have a look at the task.

Laura wants to buy a plot of land to build a house.

The table below shows some information about these plots.

So we can see that plot X has an area of 100 and perimeter of 40.

Y has an area of 120 and a perimeter of 242.

Z has an area of 120 and a perimeter of 52.

If Laura wants to build a house, which plot do you think they should choose? Pause the video and write down what your initial thought is.

Welcome back.

Let's look at part B.

By this table, you can now see plan views of the three plots.

A plan view is where you are looking down from above.

Match each image to the row in the table.

So in other words, which coloured rectangle, red, yellow, or blue matches with X, which one matches with Y, and which one matches with Z? Pause the video while you match them.

Now it's time to explain whether you'd wish to change your answer to part A.

Where should Laura build this house? Welcome back.

Now in part A, I asked you which plot you thought Laura should choose and actually you can pick whichever one you like as long as you have a reason for it.

So you might have said that you'd like Y because the area is the biggest and it also has the biggest perimeter.

You might have said Z because it has the joint biggest area and a reasonable size perimeter.

You might have said X.

And again, you might have said because you don't want a house that takes up that much space.

There are lots of reasons.

So if you'd like, you can share your reasons with either someone at home or someone in the classroom.

In this one we asked you to match the rectangle to which plot it represented.

X has to go with yellow.

Remember 10 times 10 is 100 and four lots of 10 is 40, and therefore it has to match with X.

Y matched with blue and then Z matched with red.

You can check those numbers to make sure they've matched up correctly.

Did you notice that in blue there isn't one of the numbers? Of course you can work it out yourself if you'd like.

In part C, we asked you to explain whether you'd wish to change your answer to part A and obviously that depends on what you picked initially.

Personally, I quite like the yellow one because I think my house being square makes sense.

You might of course opt for the red house.

I think it's pretty clear though that none of us is quite fancying blue.

It doesn't look like there's gonna be much room inside that house.

Let's move on to section three, the area of a parallelogram.

Now it's likely that you did this back in primary, but do you remember it? Let's make sure.

We know that the area of a rectangle is found by multiplying its length or base by its width or height.

You can actually use either of these word pairings.

We're going to use base and height here but there's actually no difference.

But the reason we're using base and height is that it's going to help with some of our future learning.

You'll see why in our future lessons.

So here's our rectangle.

We know that to find the area of this rectangle we multiply the base and height, or the longer side and the shorter side together.

If we make a cut in our rectangle and our two pieces are rearranged, what's going to happen to the area and the perimeter? Pause the video and write down what you think will happen.

Welcome back.

Let's see what you thought.

Here's an animation.

I'm cutting the rectangle and I'm rearranging the pieces.

Let's watch it again.

Does this help us to see what's happened to the area and the perimeter? What you can see here is my original rectangle and the shape I made when I cut it and rearranged it.

Notice how the base hasn't changed and the height is still exactly the same but rather than being next to the slanted side, it's showing that it's the distance between the base and the opposite length that is the same.

Our area did not change.

I didn't add anything extra to my shape, I didn't take anything away.

I can therefore conclude that the area of the parallelogram is found by multiplying the base and the height just like it was my rectangle.

I'm going to be really clear here though, and instead of just saying height, I'm going to say perpendicular height and that's because I want to be clear that it's the height from the base to the opposite side.

What it's not is that slanted length.

Now our perimeter did change.

Our perimeter is the distance around the shape and therefore our perimeter needs its slanted height, not the perpendicular height like our area.

We can use algebra to write this down in general terms. So we can say the perimeter of our parallelogram is B plus S plus B plus S where B is our base and S is our slanted height.

What you can see here are then alternative equivalent forms of what I've written down.

You may find all this algebra looks familiar to you because you've done our algebra topic and you're feeling really confident with it, but it's okay if just the first line is the one you're most comfortable with.

They all mean exactly the same thing.

The area of our parallelogram, remember, was the same as the way we found the area of the rectangle.

In other words, it's the base times the perpendicular height or B times H.

Remember with algebra, we can write that without the multiplication sign where we see the two letters next to each other, we know it means multiply.

Let's check that we can apply this.

Let's calculate the area of this parallelogram or to find the area I need the base multiplied by the perpendicular height.

So 22 lots of eight is 176.

Now it's your turn.

Calculate the area of this parallelogram.

Let's see how you got on.

That's right, in this one it's 15 multiplied by 15.

We don't want to use the slanted high at all so you should have got an answer of 225.

Now it's time for your final task.

Calculate the area of each parallelogram, pause the video while you have a go.

Welcome back.

Now let's look at part C.

In part C, we are told the area of the parallelogram is 36 square units.

Calculate the size of the missing length and then add it to the diagram.

Welcome back.

Let's just check our answers.

In A, you needed to multiply 0.

7 by 7.

3 because that's the base times the perpendicular height.

In B, this is eight times 10 because again we have base times perpendicular height.

Don't get confused by those extra measurements.

In C, you were told the area was 36, so we know that the perpendicular height times the base will give us 36, so the perpendicular height is marked as 10.

We know that 10 times something is 36, which means that our missing value must be 3.

6.

You could have marked the base as the bottom side or as the side opposite it.

So in other words, at the top of the parallelogram.

You could have marked it inside if you wanted to but most people would choose to pick one of the edges.

Let's sum up our learning for today.

The perimeter is the distance around a 2D shape.

Rectangles can look different but still have the same perimeter or same area.

The area of a parallelogram is worked out in the same way as the area of a rectangle.

Well done today.

You've worked really hard.

I look forward to seeing you for our next lesson.