Lesson video

Hello there, I'm Mr. Tilstone, and welcome to today's maths lesson, which is all about area.

We've got some wonderfully challenging problems waiting for you today, but remember two things, number one, with a positive mindset in maths, you can achieve anything, and number two, I'll be here to guide, and help you every step of the way.

So if you are ready, let's begin.

The outcome of today's lesson, what we'd like you to say at the end of it, if you've been successful, is I can calculate the area of compound rectilinear shapes.

Our keywords today, we've got two which we're going to explore now in a my turn, your turn style.

My turn, compound, your turn.

My turn, rectilinear, your turn.

Have you heard of any of those words before? I suspect rectilinear in particular might be one you've encountered recently, but let's have a recap.

A shape made up of two or more shapes, and that can be any shape, by the way, is known as compound.

And a shape where all angles are composed of right angles is called a rectilinear shape.

So for example, a rectangle is rectilinear, and a shape made up of two rectangles will be rectilinear as well, three, et cetera, et cetera.

A shape composed of two or more rectangles is called a compound rectilinear shape.

Our lesson today is split into two cycles.

The first is going to be side lengths in compound rectilinear shapes, and the second is going to be calculate the area of compound rectilinear shapes.

But let's begin with side lengths in compound rectilinear shapes.

Let's go.

In this lesson, you're going to meet these three? You might have met them before, and we've got Lucas, Sam, and Alex.

They're here to give us a helping hand.

What can you say about this shape? Well, Sam says, "It's not a rectangle." She's right, it's kind of got some rectangle properties though, hasn't it? It reminds me a little bit of one.

And Alex says, "I can see rectangles in the shape." Yes, I think I can too, can you? And Lucas says, "I can see a rectangle with a bit missing." I can definitely see that.

This is a compound rectilinear shape.

It is made from shapes that have right angles.

How could you calculate the area of this compound rectilinear shape? Well, you may have had some recent experience of calculating the area of rectangles.

That might come in handy here.

Let's have a look.

So Alex says, "I can see rectangles in the shape," yes.

"You could cut it," says Sam, "Into two rectangles," and with your mind's eye, I wonder if you could do that too.

Could you split that into two rectangles? There's no dividing lines at the minute, but could you do that with your mind? Maybe you did it like that.

There is another way to do it as well.

Lucas says, "You need to know the lengths and widths of the rectangles to calculate the area.

And at the minute we don't know that, that information is not given.

Let's have a look now, and if we've got enough information now to calculate the area.

We've got a 12 centimetre width, can't see a length, can you? And then I can see two unknown parts that maybe make up that width.

Okay, so I think not enough yet.

So Sam says, "One side is 12 centimetres long." We've got some information, haven't we? That's a start.

Alex says, "We don't know the length of the other sides." No, we could have a guess, but we don't know for sure.

And Lucas says, "The two other horizontal sides must add up to 12 centimetres." I think he's right.

So we don't know what they are, but when you add them together, they would equal 12.

Just imagine if the line at the bottom was pushed up a little bit to meet the other line, the one in the middle.

It would be the same as a line at the top, wouldn't it? We don't have enough information to know their lengths.

Now, we've got a little bit more information.

Do you think we've got enough information now to work out the missing side length? I think we have.

Sam says, "One of the horizontal sides is five centimetres long." Yes, and we know something about the top length, "The other horizontal side must be seven centimetres." Yes, and there's two ways you can look at this.

Seven plus five equals 12, or 12 takeaway five equals seven.

"But," says Alex, "We still don't have enough information to calculate the area." Can you see what's missing? Yes, we've got the width but not the length.

Or if you want to look at it the other way, the length but not the width.

But we've definitely got a missing dimension.

Okay, how about now? Got a bit more information now.

Got some length and widths.

Have we got enough information now to calculate the missing sidelines? Have a look at that, what do you think? I think we've still got something missing.

I think that's helpful, we're nearly there, but still something missing.

Can you see what it is? So "The vertical height is seven centimetres." "The other two vertical sides must add up to seven centimetres." Just like before the two sides had to add up to 12.

This time they have got to add up to seven.

Here we go.

But just like before, we've got two unknowns, so not enough information yet.

How about now we've got a four centimetre length for one of those vertical sides.

I think now we can work out what the other side must be.

Can you see it? It's quite simple arithmetic when you know what you're doing with it.

The other side must be three centimetres.

Yes, because three plus four equals seven.

Or you can look at it that seven takeaway four equals three.

But either way that will give you the missing side length of three centimetres.

Which side lengths do you need to know to calculate the area of the shape? Because we've got a lot of information there and I don't think we need all of it.

We do have enough information to calculate the total area, but possibly a bit too much.

Alex says, "We know the length and width of rectangles A and B." Yes, we do.

Yes, we do.

So A's got a length and width of seven and five, and B's got a length and width of seven and three.

Can you remember what to do with those numbers? Now Alex says, and you might have seen this too, "I saw two different rectangles." He saw it split in a different way like so, did you see that too? Have we got enough information there about the length and the width of rectangle C and D? What do you think? So which side lengths do you need to know if you split the shape this way, which are the important numbers there? What do you think we need the length and width of each of those.

Which side lengths do you need to know if you split up the shape in this way? The way you split up a shape means you need different dimensions to calculate the total area.

So in this case, look for C, we've got the length and width are 12 and three.

And for D, we've got the length and width for that as well.

That's four and five.

So they're the numbers that we need to calculate the areas of each rectangle.

Let's do a check for understanding which of the statements are true.

So have a look at that shape, we've got some information there, we've got some unknowns as well.

So which of these statements are true, number one, side E is 10 centimetres long.

Is that true? Number two, side D is four centimetres long.

Is that true? Is that definitely true? Number three, I don't know the lengths of sides D and E.

And number four, D plus E equals 14.

So which of the statements, and I'll give you a clue, it's more than one are true.

Pause the video, and have a go.

Did you come up with an agreement with the people around you on this one? Let's have a look.

Well, we don't know the side lengths of D and E, we could estimate, but we don't know for sure that information is not given.

So it's true to say I don't know the lengths of sides D and E, that's number three.

And it's also true to say that D plus E equals 14.

We just don't know the values of D and E yet, side E looks longer than side D, but we don't have enough information to say how long each side is, not yet.

Let's have another check, what can you say about sides A, B, and C? So a little bit more open-ended this time.

Have a think, have a chat, pause the video.

What kinds of things did you say? Well, all sorts of things you could have said.

Maybe you said sides A and B together are the same length as side C.

So that's the important piece of information that we wanted you to draw out from that.

And the two shorter horizontal sides must total that overall horizontal length of the shape.

That's something different that you might have said.

So A plus B has got to equal C.

Let's do another quick check.

What can you say about lines D, E, and F on this shape? Have you spotted something different by the way about this shape? It looks different, doesn't it, to the other ones that we've been looking at? Okay, pause a video, have a chat, have a think.

Let's see what you can come up with.

Okay, what kinds of things did you say there? Well you might have said sides D and E together are the same length as side F.

So D plus E equals F, you might set the two shorter sides must total the overall length of the shape parallel to them, and in this shape the sides are not horizontal and vertical.

So it looks different, doesn't it, this shape.

But we can still see it's a compound rectilinear shape.

Okay, let's have a go at some independent practise, shall we? So here's a compound rectilinear shape.

It's some true or false questions.

So have a look at that.

So number one, a, side E is 10 centimetres long.

Is that true or false? B, I don't know the length of sides d and e, is that true or false? C, d plus e equals 15 centimetres.

Number two, list the letters of the side lengths needed to calculate the area split up this way.

Question three, list the letters of the side lengths needed to calculate the area split up this way.

So which ones do you need for the area? And number four, can you work out the length that you need? Explain your reasoning.

Pause video, very best of luck, and I'll see you soon for some answers and some feedback.

Welcome back.

How did you get on with that? Number one, true or false, side e is 10 centimetres long.

That's false.

B, I don't know the lengths of sides d and e, that's true.

C, d plus e equals 15, that is true.

Number two, the letters needed to calculate the area split up in this way, a, d and e are needed, as well as the 10 centimetres.

So well done if you've got those.

Number three, the letters of the side lengths needed to calculate the area split up in this way.

So the length of sides a, b, and e are needed, as well as the 14 centimetres.

And number four, can you work out the lengths you need? Explain your reasoning, there's not enough information.

I know that a plus b equals 10 centimetres, and d plus c equals 14 centimetres, but not the length of each side.

So at the minute there isn't enough information to work out those areas.

Let's do cycle B.

Calculate the area of compound rectilinear shapes.

Let's have a look at this shape.

It's a compound rectilinear shape.

You can see it's made up of two rectangles.

How can you calculate the total area of the shape? I think we've got enough information there.

So if we separate those two shapes off, we can see we've got shape A with a length and width of seven and five, and shape B with a length and width of seven and three.

Lucas says, "How do you calculate the area of a rectangle?" Can you remember? This is something you may have had some very recent experience of doing, hopefully you have.

And Sam remembers, "You multiply the length by the width." And you might notice these are both times tables facts, seven and five and seven and three are both times tables facts.

So hopefully that's going to be automatic for you, no calculation required.

So rectangle A seven times five is 35, rectangle B, seven times three equals 21.

Now we've got to put them back together now because that's the area of each, but we want the area of the entire compound rectilinear shape.

So now we've got some adding to do 21 plus 35, and for me that's a mental calculation.

There's no regrouping or anything like that.

21 plus 35 equals 56.

So the area of the shape is 56 centimetres squared, and that's very important that we name that unit properly.

Centimetres squared.

Now same shape, but let's split it up differently.

So we're going to look at a different length and width now.

So for shape D, we're going to look at the length and width of four and five.

And for shape C, the length and width of 12 and three.

Do you think the area's going to be the same or different? The calculations are different.

Is the area going to be different as well? What do you think? Well for rectangle C, again it's the times tables fact, 12 times three equals 36.

And for shape D again, a times tables fact, four times five equals 20.

So we've got to add those together.

36 plus 20 equals 56.

The area of the shape is 56 centimetres squared.

Was that the same as before? Yes, yes, it was.

So even though we split the rectangles differently each time we had the same overall area, that didn't change.

So it does not matter how we split up the shape.

The total area will be the same.

So that's that same shape, side by side, split two different ways.

And you can see that either way it gives the same area of 56 centimetre squared.

Let's have a check for understanding, what is the total area of this compound rectilinear shape.

Now question one, do you have enough information about the dimensions to calculate the total area? And number two, which calculations will you need to work out the total area.

Pause the video and give that a go.

So here we go, seven plus eight equals 15.

So we needed to do a little bit with the numbers that we'd got there to work out the length or width of that side, but we did have enough information to do it.

So seven plus eight equals 15, and then 15 takeaway five equals 10.

So again, we had enough information but we needed to do a little bit with it to get the dimensions that we needed to work out the area of that shape.

So yes, there's enough information, but it was quite hard work there wasn't it? Which calculations will you need to work out, the total area, 15 times five equals 75.

That wasn't a times tables fact, and seven times 10 equals 70, that was one.

Okay, are you ready for some practise? Let's have a look.

So number one, calculate the total area of this compound rectilinear shape.

So have a look at that.

Think about the information you've got.

You might need to do a little bit with some of it.

And Alex is saying, "Which dimension is missing, and how will you work it out?" So you've gotta use some logic there.

Number two, calculate the missing dimensions needed.

And then the area of these compound rectilinear shapes.

So you are going to have to split those shapes up yourself.

There's a lot of information there.

Some of it might not always be the information that you need.

You might need to do a little something to it.

But see if you can work out the area of each shape, and if you can, find more than one way to calculate the total area for each shape, 'cause for each of those shapes I could split it up two different ways into rectangles.

Very best of luck, and I'll see you shortly for some feedback.

Off you go.

Welcome back.

How did you get on with that? Let's have a look.

So calculate the total area of this compound rectilinear shape.

It was made up of two rectangles, it's compound rectilinear.

So the area of the top rectangle, 25 times five is 125 centimetre squared.

The area of the bottom rectangle, which we need to do some calculations to get is five times 10, which is 50.

Now we've gotta put those together, and that gives us 175 centimetre squared.

Brilliant if you got that.

And number two, the missing dimensions needed, and the area of the compound rectilinear shapes.

Well we could do this.

So two times five equals 10 centimetres squared, 10 times six equals 60 centimetres squared.

And then add them together, and we've got 70 centimetres squared.

You might have done it this way though, 11 times two equals 22 centimetres squared, six times eight equals 48 centimetres squared.

Add those together and we've got 70 centimetres squared.

And for B, six times nine equals 54 centimetre squared, six times four equals 24 centimetre squared.

Add those two areas together, and we've got 78 centimetre squared.

But you might have done it this way, six times five equals 30 centimetres squared, 12 times four equals 48 centimetre squared.

And then add those together, 30 plus 48 equals 78 centimetres squared.

Congratulations if you've got that.

For C, we've got six times eight equals 48 centimetres squared, 12 times 7 equals 84 centimetres squared.

48 plus 84 equals 132 centimetres squared.

Or six times 20 is 120 centimetres squared, 12 times one equals 12 centimetres squared.

Add those together, that gives us 132 centimetres squared.

We've come to the end of the lesson, and it's been wonderfully challenging.

I hope you've enjoyed it, I certainly have.

A shape composed of more than one rectangle is called a compound rectilinear shape.

The shorter sides of a compound recline shape in a particular direction can be added to get the overall length or width of the shape, the area of a compound rectilinear shape can be calculated by splitting the shape into rectangles, calculating the area of the rectangles, and then adding the areas together.

Now, sometimes that's relatively straightforward, because the the exact information is there and nothing else, but sometimes there's not enough information, sometimes there's too much information.

So we've got to be careful that we're using the exactly the right dimensions and multiplying those together.

Very well done today.

It's been a great pleasure working with you, and I do hope to see you again soon for some more maths.

But until then, take care and goodbye.