Lesson video

Hello everybody.

My name is Mr. and welcome to today's lesson on calculating the area of rectilinear shapes.

Now, before we start, you will need a pen, a piece of paper, and a ruler.

Also, please try to find yourself a quiet place.

Somewhere that you won't be disturbed.

And don't forget to remove any sorts of distractions.

For example, turn off your mobile phone or move it away, completely away.

Pause the video.

And then when you're ready, let's begin.

Today's lesson is about calculating the area of rectilinear shapes.

We will be looking at two strategies to solve this and then we'll take our independent task.

And as I've mentioned, you'll need a pencil, ruler, and some paper.

Now, to start with: decide if the following are measures of area, length, or perimeter.

Pause the video.

And when you're ready, press play to continue.

Well, first one is the distance a javelin is thrown because it's a distance it's measured in all length.

The second one is all to do with this turf needed to cover a football pitch.

So we're talking about area and surface area.

And the third one is to do with the outside of a shape - the distance around the outside of a shape - and it's to do with perimeter.

These are rectilinear shapes.

How can you describe them? Pause the video.

Take a few minutes to think about it.

Press play when you're ready to continue.

So we could say a few things about these shapes.

We could say that all the sides meet at a right angle.

We could also say that they can be split into rectangles, too.

We could count the squares inside to find out the area of the shape.

We could measure - we could count or measure the distance around the outside of the shape to find the perimeter of the shape.

On the screen, you have two rectilinear shapes which are exactly the same.

Have a think: How would you find the area of these shapes? Pause the video.

When you're ready, press play to continue.

Okay.

Couple of methods.

The first method is I could count the squares inside the space.

And that's great when you've got small shapes or part shapes but it's not so great when we've got bigger shapes or we don't have squares inside the shapes.

For example, if you're measuring a pitch frame and you want to know the area, you wouldn't have squares naturally inside the shape - you'd just have lengths to the side.

So let's presume that we don't have squares inside.

We just have lengths to the side.

So first thing we can do on the first one: we could imaginary split the shape into two rectangles.

And now that I've got two rectangles, I know how to find the area of each rectangle because I'm looking at the length multiplied by the width.

So for my first rectangle, I know that I've got a length of four centimetres and a width of two centimetres.

So two by four is eight centimetres squared.

And coincidentally, the second one is two by four which is also eight centimetres squared.

So if I add the first shape and up the second shape, I get the total area of the whole shape which is 16 centimetres squared.

I can do the same thing, but in a different way.

So looking at shape number two, I could split it differently this time.

I've still got two, I've got a rectangle and I've got a square, and I know how to find the area of both of those shapes.

So just thinking about this, I know that my length of the top rectangle is six centimetres and it's two centimetres deep, or two centimetres wide, so the area is 12 centimetre squared.

And I know the square at the bottom is a two by two square, which is four centimetres square.

So in total, 12 centimetres squared and four centimetres squared gives me an area of 16 centimetres squared.

You can see that I've got two different ways to calculate this.

What they give - they both give me the same answer.

Like I said, you've got a third where you can count the squares inside.

And if you count them, you'll still get 16 centimetres squared.

Have a loot at these shapes.

Try to split the rectilinear shapes and calculate their area.

Pause the video.

And then when you're ready, press play to continue.

So you may do this differently than I do it, but you will still get the same answer.

So I've decided to split the shape into - the first shape - into a five by three rectangle on a two by two square.

So I'm going to multiply five by three which gives me 15 centimetre squared, two by two which is four centimetres squared; up them together, and my area is 19 centimetres squared.

You might have done it differently.

You might have split the shape down the line in the middle and had a three by three centimetre square and a two by five cen- uh two by five centimetre rectangle.

So three by three square is nine centimetres squared.

The five by two is 10 centimetre squared.

Add those together.

Gives you 19 centimetres squared.

Okay, moving on to shape number two.

So I've decided to split it this way.

And this time, we're measuring in millimetres rather than centimetres.

So I can see that I have a three by five millimetre rectangle, and I have a four by two millimetre rectangle.

Three by five is 15 millimetres squared, four by two is eight millimetres squared, gives me a total of 23 millimetres squared.

I wouldn't have done this a different way.

Because if you do a different way, you end up with potentially three shapes.

And three shapes is more difficult than two shapes.

So I like to stick with as minimal shapes as possible.

Okay.

Example number - example C.

This time, we do have to have three shapes.

So I've split it this way.

I've got to by one, another two by one, and a four by two millimetre.

And add all these together, I got two millimetres squared, two millimetres squared, and eight millimetres squared, which gives me 12 millimetres squared.

The main learning from this slide is that you can find the area of rectilinear shapes by calculating them.

And you need to split the shape into different ways.

It doesn't matter how you split the shape, but as long as you can split the shape, you can find the area.

For the slight back to how it was at the start, I just want to remind you that if you need to find a missing side, you can do this: So I've been told that this length at the top is five centimetres.

If I know this is two centimetres, but I don't know the length of this side - and let's imagine from now, we don't have squares.

So we can't count.

What I can do is, say, well I've got five centimetres in total.

I've used two of those centimetres.

So this must be three centimetres left.

And it's the same way.

If you look at example number two: I've been told this is five, and this is two, and this is one.

I need to find this missing side.

So I can say I've got five millimetres.

I've used one.

I've used another two.

That's a total of three millimetres, which means I've got two millimetres left.

So sometimes you need to find the missing side on one of these shapes, and that will help you calculate this area.

So far, we've looked at one way of finding the area of a rectal linear shape.

We've looked to taking the whole shape and splitting it into different parts; finding the individual parts to give you their - the whole shape.

Well, now look at the second method.

So here we have a rectangle- sorry, it's not a rectangle - but if we- if we know that it's five metres long - if we can create a whole rectangle, which is five metres by four metres, and find out the area of the whole rectangle, which is 20 metres squared, we can then just simply subtract the other two metres which we're not using.

Essentially I've circled- I've got a five by four rectangle there, which is 20 centimetres- 20 metres squared, And I'm not using those two.

So I have done 20 metre squared, takeaway two metres squared, gives me 18 metres squared.

It could still do it the other way as well.

I could tell I'm going to split the rectangle there, and now I've got a five by three rectangle which is 15 metres squared.

And I've got a one by three, which is three metres squared.

So in total, I've got 18 metres squared.

It doesn't matter which way you do it.

You might find one way works better for you.

You might find a particular shape works better for one way than it does another way.

But have a look at a shape, think about which strategy is the best way to approach it.

On the screen, you now have two images.

Try to use the second strategy where you count the full rectangle and take away the missing parts.

Pause the video.

And when you've got your answers, press play to continue.

So I can say in my first shape: I've got a length of seven and the width of six, so a total area of 42 kilometres squared.

There's two kilometres squared that I'm not using, therefore my entire area is 40 kilometres squared.

Similar in the second example, I've got a five by six rectangle.

So the area is 30 centimetres squared.

However, I'm not using two centimetres squared so total area is 28 centimetre square.

Now it's time for your independent task.

Pause the video, complete your task, and press play when you're ready to continue.

Looking at the two shapes on the screen, I'm going to solve the first shape by looking at the individual rectangles within the shape and then adding these up.

And rectangle B: I'm going to look at the overall rectangle and then take away a part of the rectangle.

So rectangle A: I can see I've got a five by four kilometre rectangle- excuse me, 20 kilometre squared, and I've got another four by two kilometre rectangle which is eight kilometres squared.

The total area of this compound shape is 28 kilometres squared.

For rectangle B, I'm going to look at the shape number B, I'm going to look at the overall shape, and I'm going to say, well, that's a four by seven rectangle, which is 28 centimetre squared.

But I'm not using a one by one square which is one centimetre squared.

So the total area is 27 centimetres squared.

So this is C.

We're going to take the overall rectangle, which is a seven by five millimetre rectangle, which is 32 millimetre squared.

And we're going to take away the two by one rectangle which is two millimetres squared.

So the total area of shaped number C is 33 millimetres squared.

Shape number - shape B: We're going to split into two rectangles.

So I have a four by two rectangle which is eight metres squared.

And I have a three by one rectangle which is three metres squared Add them together - gives me an area of 11 metres squared.

Shape E: I'm going to split into three separate shapes - three shepar- separate rectangles.

Rectangle number one is a seven by three which is 21 kilometres squared.

Shape number two is five by one - five kilometre squared.

Shape number three - six by one - six kilometres squared.

Add them all together.

Gives us the total area of 32 kilometres squared.

Just having a look at shape E, we'll notice that I wasn't given this length here.

However, I know that the area- the length of this is five kilometres.

This is three kilometres.

This is one kilometre.

So three and one is four, five, take four.

This most be one kilometre in length.

In order to find this missing length here: all I know that in total, the length is seven kilometres.

I've used two kilometres.

And at this point, I'm presuming that last halfway, so this must be the length of one.

That means that this length here must be six kilometres.

For shape number F I'm going to start with the overall shape of the rectangle - are five by six, right? which is 30 millimetres squared.

And I'm going to take away the small rectangle inside, which is a two by one, which is two millimetres squared.

That gives me an area of 28 millimetres squared.

Congratulations on completing your task.

If you'd like to, please ask your parent or carer to share you work on Twitter, tagging @OakNational and also #LearnwithOak.

Now before we go, please complete the quiz.

So that brings us to the end of today's lesson on calculating the area of rectilinear shapes.

A really big bold on to all the fantastic learning that you've achieved.

Now before you finish, perhaps quickly review your notes and try to identify the most important parts of your learning from today.

Well, all this left for me to say is thank you.

Take care and enjoy the rest of your learning for today.