Lesson video

Hi there.

My name is Mr. Tillston.

If I've met you before, it's nice to see you again and if I haven't met you before, it's nice to meet you.

Today we're going to be looking at parallelograms and the area of parallelograms. That might be something that you've had some recent experience with.

You might already know a little bit about that.

Let's see if we can take that one step further, shall we? If you're ready, I'm ready.

Let's begin.

The outcome of today's lesson is I can use the area of a parallelogram formula to calculate unknown measurements.

So can you remember how to calculate the area of a parallelogram? We've got some key keywords.

My turn, parallelogram, your turn.

My turn base, your turn.

And my turn, perpendicular, your turn.

I think you've probably heard those words before.

Hope you have.

You might just need a little reminder about what they mean because they're very important and they're going to come up a lot today.

So a parallelogram is a quadrilateral with 2 pairs of parallel and equal sides.

And you can see an example on your screen now.

The base is the side which is perpendicular to the shape's height.

And you might know or might remember that a base can appear in different points on a parallelogram.

And 2 lines are perpendicular if they meet at a right angle.

And you can see an example there.

In fact, there are 2 examples there on the screen in front of you.

Our lesson is split into 2 cycles.

The first will be, use division to find the perpendicular height and the second, use division to find the unknown base.

So in today's examples, we're going to tell you the area of the parallelogram already and you've gotta work out the missing information.

We're gonna start by having the perpendicular height missing and then after that, the base missing.

Let's see if we can do that.

In today's lesson, you're going to meet Aisha, Andeep and Lucas.

Have you met them before? They're here today to give us a helping hand with our maths and very helpful they are too.

Any perpendicular line drawn from a selected base in a parallelogram to the height of the opposite vertex shows the perpendicular height.

So that's an example of a base and the line that's parallel to that is also the base.

And that's one of many places where we can show the perpendicular height.

So you can see a perpendicular line there, hopefully you can see the right angle.

There we go.

A formula can be used to calculate the area of a parallelogram.

So can you remember how to do it? What do you do with the base and the perpendicular height? To calculate the area of a parallelogram, multiply the base by the perpendicular height.

That's not the formula, that's how to do it.

That's a formula.

So base times perpendicular height equals area.

You might also say area equals base times perpendicular height.

You could even say area equals perpendicular height times base, lots of ways to say that.

But for now, let's say base times perpendicular height equals area.

Can you say that with me? Let's go.

Base times perpendicular height equals area.

Now just you.

Ready, go.

So that's our very important formula that we're using today.

So in this case, the base is 5 centimetres, the perpendicular height is 3 centimetres.

Some nice easy arithmetic here for you.

Multiply those numbers together and we've got 15 centimetres squared.

That's the area of that parallelogram.

Now have a look at this.

What's the same and what's different about these examples? So have a look.

They look very similar at first glance, don't they? Have a look though.

Hmm, what can we say? Well, in the first example, the area is unknown.

In the second, the perpendicular height is unknown, but the area is known.

What formula could be used each time? So let's think about that one that we've just explored before, because we don't know the area, but we do know the base and we do know the perpendicular height.

So what formula can we use? Base times perpendicular height equals area.

So in this case, 5 centimetres times 3 centimetres equals something centimetres squared.

And let's have a look at the other parallelogram.

We can still use that same formula.

Base times perpendicular height equals area, even though we don't actually know the perpendicular height.

Lemme show you what I mean.

We know the base, that's 5 centimetres.

We don't know the perpendicular height.

So let's just leave that blank.

And we know the area, that's 15 centimetres squared.

So it turns into a sort of times tables fact with a bit of information missing.

5 centimetres times something centimetres equals 15 centimetres squared.

Now we can look at it a different way.

We know the area.

So we could do area divided by base equals perpendicular height.

It will give us the same number whichever way we do it.

That's 15 centimetres squared divided by 5 centimetres equals something.

The missing perpendicular height can be the missing number in a multiplication equation, just like the one we just saw.

Say look, we've got the area.

We know the area is 60 centimetres squared.

We know the base that's 10 centimetres.

Remember base times perpendicular height equals area.

That's our main formula that we're working from today.

That means 10 centimetres multiplied by something centimetres that's missing, equals 60 centimetres squared.

So it's a multiplication equation with a bit of information missing.

Or using the inverse it could be determined by division.

Area divided by base equals perpendicular height.

So let's put some numbers to that one.

Numbers would fit into that formula.

That would be 60 centimetres squared divided by 10 centimetres equals something centimetres.

And in either case the answer is 6 centimetres.

So 2 ways to get to the answer of 6 centimetres.

That is the missing perpendicular height.

Let's have a check.

The area of the parallelogram is 27 centimetres squared.

What's the perpendicular height? So think about the formula that you know, think about how you could use that.

How could you change it a little bit, maybe? What could you do to find that missing perpendicular height? Pause the video.

Well, I can think of 2 different ways to solve this.

One as a multiplication equation and one as a division.

So base times perpendicular height equals area.

We know the base, we know the area, we don't know the perpendicular height.

So that's 9 centimetres multiplied by something equals 27 centimetres squared.

So that's a missing number.

Or we could look at it as a division.

That's area divided by base equals perpendicular height.

That means 27 centimetres squared divided by 9 centimetres equals something.

Which way did you do it or did you do it both ways? Well, either way the answer is 3.

So the missing perpendicular height is 3 centimetres.

Well done if you've got that, you're on track.

It's time for some practise.

Number one, the areas and the bases of the following parallelograms are given.

So all the way through, you know the area, you know the base.

Calculate the perpendicular height.

Be careful, there are some red herrings in here.

Some of the questions, I've got 3 measurements given, but you only need 2.

I've got some more examples here.

On D the perpendicular height hasn't been drawn.

And one final example here.

Right here, best of luck with that and pause the video.

See you soon.

How do you get on finding those missing perpendicular heights? Did you apply the formula and select the correct information? In A, you didn't need that side length of 3 centimetres.

You needed the area that was 10 centimetres squared and you needed the base, that was 5 centimetres.

So 10 divided by 5 equals 2.

So that's 2 centimetres for the missing perpendicular height.

And for B, something multiplied by 12 equals 96 centimetres squared, or 96 centimetres squared divided by 12 equals something and the answer is 8.

So that's the missing perpendicular height there.

Hopefully you weren't fooled by the fact that the base is vertical.

And for C, did you spot the red herring again? We don't need that 11 centimetres.

We do need the area, that's 150 centimetres squared and we do need the base and that's another vertical base, that's 15 centimetres.

So 150 divided by 15, or 15 multiplied by something equals 150 and the answer is 10.

So it's got a perpendicular height of 10 centimetres.

And then for D, you might have drawn your own perpendicular height in.

The area was 1,600 centimetres squared and the base was 80 centimetres.

Now you might have used some known facts flag, but the answer is 20 centimetres, that's the perpendicular height.

And for E the area is 108 centimetres squared.

18 multiplied by 6 equals 108.

So that was beyond our times tables.

Hopefully you use some different multiplication skills to get there.

Are you ready to move on? You're doing really well.

Well let's crack on and let's look at using division to find the unknown base.

So you've known the area and you've known the base and you've been finding the missing perpendicular height.

This time you're going to know the area and the perpendicular height and you're going to find the base.

Again, let's have a look at this.

What's the same and what's different about these examples? Have a good look.

Have a close look.

They look very similar at first glance, but they're not identical.

They've got different pieces of missing information, some similar known information there.

In both examples, the area is known, so it's 60 centimetres squared.

In the first example, the perpendicular height is unknown.

In the second example, the base is unknown.

What formula could be used each time? So you've got some experience of the example on the left.

You've done that in the first cycle.

So what could we use for that? Can you remember? Can you think about that? We could use that really useful formula, base times perpendicular height equals area.

That's 10 centimetres multiplied by something equals 60 centimetres squared.

Or we could think of it as division, area divided by base equals perpendicular height at 60 centimetres squared divided by 10 centimetres equals something.

And in the second one there was some different unknown information and some different known information for that matter.

We could still use that very helpful formula there.

Base times perpendicular height equals area.

That's something centimetres, because we don't know the base do we, multiplied by 6.

That's a perpendicular height that we do know, equals 60 centimetres squared.

What about division? What could the formula be for that? That could be area divided by perpendicular height equals base.

And again, both will get you the answer.

So what numbers would fit that formula? In this case 60 centimetres squared divided by 6 centimetres equals something centimetres.

Okay, let's have a look at an example, shall we? This parallelogram has got an area of 55 centimetres squared so that we know, and it's got a perpendicular height of 5 centimetres, so that we know, we just don't know the base.

The missing base can be the missing number in a multiplication equation.

Base times perpendicular height equals area.

I quite like this method.

That's something centimetres multiplied by 5 centimetres equals 55 centimetres.

What's the missing number there? Or using the inverse, it could be determined by division.

What would the formula be? That's area divided by perpendicular height equals base.

So what would the numbers be? That's 55 centimetres squared divided by 5 centimetres equals something centimetres.

And either way the answer is 11.

So our missing base is 11 centimetres.

Well done if you got that.

Let's put all of this to the test, shall we? Let's have a look and do a check from this standing.

The area of the parallelogram is 60 centimetres squared.

Calculate the length of the marked base.

So think about what you know, think about what you don't know, think about how you could find what you don't know.

Pause the video.

I wonder did you use division or did you think of it as a missing multiplication equation? Hmm? If you did, the formula will be base multiplied by perpendicular height equals area.

Now we don't know the base, we do know the perpendicular height and we do know the area.

So that's something centimetres multiplied by 5 centimetres equals 60 centimetres squared.

I see a times tables fact there, do you? Or we could use division.

Which did you do? Did you do both? That's area divided by perpendicular height equals base.

So what will the numbers be here? That'll be 60 centimetres squared divided by 5 centimetres equals something centimetres.

Either way you get the answer 12 centimetres.

Well done if you've got that, you're on track.

Time for some final practise.

Number one, the areas and perpendicular heights of the following parallelograms are given.

They're not drawn to scale.

Work out the base of each.

So we know the area this time, we know the perpendicular height.

Need to work out the base.

Be careful there are some red herrings here.

And some more examples here.

And some final examples here to tackle.

You might notice something slightly different about F.

And number 2, the Principal of Oak Academy loves parallelograms. Who doesn't? And is planning to instal a new AstroTurf section on the playground in the shape of a parallelogram.

The turf costs 14 pounds per square metre and she spent 2,800 pounds.

Now straight away my brain noticed a link between those 2 numbers.

That's all I'm going to say.

She's invited class 6 to make suggestions for the shape.

Who could be right? Well let's see what they've got to say.

This is what Aisha says.

It could be a square with sides that are 20 metres in length.

Could it? Lucas says it could be a parallelogram with a 20 metre base.

Could it? And Andeep says it could be a parallelogram with a perpendicular height of 800 centimetres.

Could it? Okay, have a think about that.

There's a few different steps involved in this problem.

So do take your time with it, have a really good think about it.

The answer won't come to you straight away.

Persevere with it.

Okay, pause the video.

Good luck with that and I'll see you soon for some feedback.

Welcome back.

How did you get on with that? That last question was a bit of a head scratcher, wasn't it? I hope you enjoyed that challenge.

I love that kind of problem.

Well number one, the areas and perpendicular heights are given and we're going to work out the base of each.

So you might have noticed in that first one we didn't need that 5 centimetre side length.

That was a red herring.

But we did need the area, that's 40 centimetres squared and we did need the perpendicular height.

That's four centimetres.

And whether we use multiplication or division gives us an answer of 10 centimetres.

And for B, the arithmetic's a lot more challenging for this one, isn't it? But we still use the same method.

So we do know the area 336 and we do know the perpendicular height.

That's 14 centimetres.

So we can either treat it as a multiplication equation with missing information or we can treat it as division.

Whichever way you did it, the answer is 24 centimetres.

And for C, we know the area is 504 centimetres squared and we know the perpendicular height's 18.

Again, this is well beyond times tables, isn't it? But maybe you used a written method, I suspect you did.

The answer is 28 centimetres because 18 multiplied by 28 equals 504.

And likewise 504 divided by 18 equals 28.

And then for D, 600 metres squared, did you spot that? And 20 metres.

And 20 multiplied by 30 equals 600.

So that's the missing base.

And for E, 243 centimetre squared was the area and 9 centimetres was the perpendicular height.

You might have noticed that the base was presented vertically this time.

9 times 27 equals 243.

You might have used a written division method for that.

I suspect you did.

That's what I would've done.

And then for F, what did you notice about this? Something a bit different.

Well, a couple of things.

Number one, it's in a different unit that's metres.

And number 2 is a decimal.

But those numbers were related.

There was a relationship between those numbers.

And it reminds me of times tables fact does it here.

I could see 5 multiplied by something equals 72 there, but 0.

8 multiplied by 0.

9 equals 0.

72.

Well done if you got that, that was quite tricky.

And this lovely meaty final question.

So the principal loves parallelograms and she's planning to instal a new AstroTurf section on the playground in the shape of a parallelogram.

The turf costs 14 pounds per square metre and she spent 2,800 pounds.

Now my first job there would've been to work out how many square metres she's got.

If that's how much she spent and that's how much it costs, we can do something with those numbers, we can use division.

Now there's a nice relationship between those 2 numbers, isn't there? 14 and 28 is what I saw there.

So I know 14 goes into 28 twice.

And that was a good starting point.

So 2,800 divided by 14 equals 200.

So the head teacher has 200 square metres of AstroTurf.

So that was our first kind of hurdle to get over.

So now we know that we can check what everybody's got to say.

So Aisha said it could be a square with sides that are 20 metres in length.

True or false? No, that's not true.

20 metres multiplied by 20 metres equals 400 metres squared.

So there will not be enough AstroTurf for that.

Not by a long way.

Sorry, Aisha.

Let's see what Lucas said.

He said it could be a parallelogram with a 20 metre base.

Well, 2,800 divided by 40 equals 200 as we've established.

So the head teacher has 200 square metres of AstroTurf as we've established.

200 divided by 20 equals 10.

So it could be any shape parallelogram with a base of 20 metres and a perpendicular height of 10 metres.

Perhaps you could sketch some possible designs.

But yes, Lucas, you were right, it could be a parallelogram with a base of 20 metres.

And Andeep said it could be a parallelogram with a perpendicular height of 800 centimetres.

Did you notice he said centimetres not metres? But we can convert that.

800 centimetres equals 8 metres.

So it could be any shape parallelogram with a perpendicular height of 8 metres and a base of 25 metres.

And again, perhaps you could sketch some possible designs.

But well done if you're able to recognise what the base was.

We've come to the end of the lesson.

I've really enjoyed that lesson.

It's been nice and challenging and I hope you've enjoyed that.

So today we've been using the area of a parallelogram formula to calculate unknown measurements.

If the area of a parallelogram is known and either the perpendicular height or the base is known division can be used to calculate the missing measurement.

And we could say area divided by base equals perpendicular height, or we could say area divided by perpendicular height equals base.

Well done on your achievements in today's lesson.

You've been fantastic and you definitely deserve a pat on the back.

So that's your next task.

Give yourself a pat on the back.

Hopefully I'll get the chance to spend another maths lesson with you in the near future.

But until then, take care.

Enjoy the rest of your day, whatever you've got in store and goodbye.