Lesson video

Today we'll be looking at solving problems involving the calculation and conversion of units of area.

All you'll need is a pencil and piece of paper.

So pause the video and grab your things if you haven't done so already.

Our agenda for the lesson looks like this.

We're solving problems involving the calculation and conversion of units of area.

First of all, we'll start with a quiz to test your knowledge from our previous lesson, then we'll look at understanding the relationship between square millimetres, centimetres and metres, then apply this to calculating area and then a final independent.

So let's start with your initial knowledge quiz.

Pause the video now and complete the quiz and click restart once you're finished.

So the first question I want you to think about is this, what is one centimetre square in millimetres squared and why? And how can you prove this? I'd like you to pause the video now and make some notes about this question.

So my thinking is that if one centimetre is equal to 10 millimetres, then is one centimetre squared equal to 10 millimetres squared? Let's have a look at this pictorially to help us to visualise what we're talking about here.

So I've got some graph paper and this shows that within one centimetre square.

So this square here, the black square represents one centimetre square.

And within this, there are a hundred of the smaller squares is 10 across and 10 down so there's a hundred within it all together.

And the small squares, they have an area of one millimetre squared, that's because they measure one millimetre across and one millimetre up, therefore their area is one millimetre squared.

So within this one centimetre square there are 100 of these one millimetres squares, therefore one centimetre squared is equal to 100 millimetres squared.

And then if we actually think about this as we did in our previous area lessons, if we converted one centimetre into millimetres, that would be 10 millimetres.

And then to find the area in millimetres, we would be multiplying 10 millimetres by 10 millimetres, which is equal to 100 millimetres squared.

Now let's look at applying this further.

So now we know that one centimetre squared is equal to 100 millimetre squared.

How many centimetres squared are equal to one metre squared? Pause the video and have a think about this question.

So we know that one metre is equal to 100 centimetres.

Therefore one metre squared is equal to 100 centimetres multiplied by a hundred centimetres which is 10,000 centimetres squared.

So this is a lot of thinking for us to get our heads around.

And we have to think about when we're approaching our problems whether initially we want to convert the measure into our final desired unit, or whether we want to do that afterwards.

So let's have a look at how we apply this relationship to calculating area.

So here we have a compound rectilinear shape and we're being asked to first of all calculate the perimeter in millimetres and then the area in square millimetres.

So let's begin with the perimeter.

We're looking at the distance all the way around the shape.

We're being given a units in centimetres but we're asked for our answer in millimetres so we have two ways of approaching this.

First of all, we could calculate the perimeter in centimetres and then convert to millimetres by multiplying by 10, or we can calculate, we can convert all of these measures into millimetres and then we will already have our answer in millimetres.

So the way I've done it here is I've used the original units, which are centimetres and then I've converted it afterwards.

So I've added the measurements of all of the sides together and found a perimeter of 12 centimetres, I then multiplied the 12 centimetres by 10, which gives me an answer of 120 millimetres as the perimeter.

Now, if you had converted these in the first place to millimetres, so that will be 10, 30, 10, 20, and so on.

You would have come to an answer of 120 millimetres as well.

So perimeter is really straightforward.

You can either convert in the first place or afterwards.

Let's have a look at the area.

So we'll start off by looking at the area of rectangle A.

So rectangle A has an area of three square centimetres.

It's got a height of three centimetres, a width of one and three times one is three centimetre squared.

Now I know that one centimetre squared is equal to 100 millimetres squared.

Therefore I know that three centimetre squared is equivalent to 300 millimetres squared.

So in this instance, I've kept it in centimetres and then I've converted it to millimetres afterwards.

And you notice that unlike the perimeter where I just multiplied it by 10, this time I have to multiply it by 100, because I'm multiplying two dimensions here, that will be 30 millimetres by 10 millimetres.

And I'll demonstrate this with the second strategy for rectangle B.

So for rectangle B, if I convert to millimetres, two centimetres is 20 millimetres, and one centimetre is 10 millimetres.

20 multiplied by 10 is equal to 200 millimetres squared.

So I've given you two different strategies there.

And finally, as this is a compound rectilinear shape, we have to add the two areas together to get the total area of 500 millimetres squared.

Now, I want you to think about these two approaches when you have a go at this shape in calculating the area in square millimetres.

So what you could do for rectangle A is to calculate the area in centimetre squared and then convert to millimetre squared.

And then for B, you could convert the measurements here into millimetres in the first place, and then your answer will be straight away in millimetres squared.

So pause the video now and calculate the area of the shape.

So, your approach for A was to calculate in centimetres first and then convert.

So two centimetres multiplied by one centimetre is equal to two centimetres squared.

So it has an area of two centimetre squared.

Now we know that one centimetre squared is equal to a hundred millimetres squared.

Therefore two centimetre squared is equal to 200 millimetres squared.

For B, we use the second strategy.

So one centimetre was converted to 10 millimetres, and three centimetres converted to 30 millimetres, 10 times 30 is 300 millimetres squared.

And then your final job to do here was to add those two areas together, which gives you an area in total of 500 millimetres squared.

We're going to do another one together because this is a tricky concept to get our heads around.

So here we've got another different looking problem.

And I think if you're feeling confident, you could pause the video and have a go at this yourself.

So the question is to calculate the area of the blue area and the purple area and to give your answer in millimetres squared.

So if you're feeling confident, pause the video now and then we'll go through it together and if you still need a bit more support with this, no problem at all, just keep watching as we go through the strategy.

So, first of all, we're looking at the blue area and I'm using my first strategy where I calculate in centimetres and then I convert to millimetres.

So the blue rectangle is 36 multiplied by 42 centimetres which is 1,512 centimetres squared.

And I know that to calculate from centimetre squared to millimetres squared, I have to multiply by a hundred.

So 1,512 centimetre squared multiplied by a hundred gives me 151,200 millimetres squared.

Now let's do the area of the purple part using our second strategy.

So the purple section was nine centimetres or 90 millimetres by 42 centimetres or 420 millimetres.

And therefore our answer was 37,800 millimetres squared.

Now the one last thing to do is to go back to the area of the blue, because this is not the true area of the blue part because the purple needs to be subtracted from that to tell us the area of the blue part.

So we find the difference between the blue and the purple part, and that gives us an area for the blue part of 113,800 millimetres squared.

Okay, it's time for you to do some independent learning.

So pause the video and complete the task and then click restart once you're finished and we'll go through the questions together.

So for question one, you are given three identical rectangles that have been used for a compound rectilinear figure and you were asked to calculate the area in centimetre squared.

Now the first job was to find out the actual dimensions of each rectangle.

So you are given this dimension of 12 millimetres which we know is also this dimension here, but you weren't given the height of the shapes and the way to do that with was to look at whole measurement of 65, subtract the 12 millimetres from it, and then divide it by two to find these measurements.

So now we've got the dimensions.

Each shape measures 12 millimetres by 26.

5 millimetres.

So you do 12 times 26.

5 and then multiply it by three because there are three of those shapes all together, and that gives you 95 millimetres squared.

Now to convert to centimetres squared you have to then divide your answer by a hundred which gives you 9.

54 centimetres squared.

The other way you may have done it was to turn these initially into centimetres.

So 2.

65 centimetres multiply by 1.

2 centimetres, which gives you 9.

54 centimetres squared.

For question two, you have got the plan of a new zone at the Space Centre.

And we're asked to calculate this in centimetres squared.

And you were given your initial measurements in metres squared, no just in metres.

You are going to calculate the area in metres squared.

So again, I'm finding the missing measurements that I haven't been given yet or adding them on.

So I know that this whole width here is 28 metres and this section is nine metres, so I subtracted nine from 28 and then divided that by two to find the measurements of these two, which is 9.

5.

And then this whole width is 35 metres with a small section of 19 metres.

So this part here for which is applied to this shape is 16 metres.

So job number one was to find all of the different dimensions and then to start to calculate the areas of the different shapes.

So this is for the top and the bottom shape.

35 multiplied by 9.

5 and then times two because there's two of them is 665 metres squared.

And then this middle shape was nine metres by 16 metres which gives us 144 metres squared.

Then we've added these two numbers together to give us the total area of 809 metres squared.

And we know that one metre squared is equal to 10,000 metre squared.

So we have to multiply 809 by 10,000, which gives us an area of 8,090,000 centimetres squared.

So here we have a design created by Liman using five identical rectangles.

First of all, we were asked to find the area of the grey section in millimetres squared, and then the total area of the blue section in centimetre squared.

So first of all, we're looking at the grey area which is made of three triangles.

So to calculate the area of the triangles, we do width multiplied by perpendicular height.

So that 70 millimetres multiplied by 11.

5 centimetres which I've converted to millimetres, so that's 115 and then divided by two.

So that's 115 multiplied by 70 divided by two, 115 multiplied by 70 is 8,050, divided by two is 4,025 millimetres squared.

And then multiply by three because there's three triangles, that's 12,075 millimetres squared.

So that's the answer to your first part of the question.

The second part is what is the total of the blue area of Liman's design? And that's made up of one, two, three, four five identical rectangles.

So that was 70 millimetres multiplied by 115 millimetres to find the area of one and then multiplied by five.

So we already know 115 times 70 is 8,050 and multiplied by five is 40,250 millimetres squared.

Now we need to remove the grey areas from that.

So 40,250 subtract the grey area which was 12,075.

So that gives us an area of 28,175 millimetres squared.

And to convert that to centimetres we divide by a hundred, which gives us 281.

75 centimetres squared.

Really well done today.

That was such a tricky lesson to get your head around but I'm very impressed with your persevering.

In our next lesson we'll be calculating the volume of cubes and cuboids.

I'm looking forward to seeing you then.