Lesson video

Hello, my name is Mr. Southall and in today's maths lesson, we're going to be looking at finding the area of non-rectilinear shapes.

Before we start, please try and make sure that you are in a safe environment that is free from distractions such as mobile phones.

If you can put any devices on silent, that would be best for your learning and you'll need a pencil and paper for today's activities.

Now do remember you can pause and rewind the video at any time.

So if there's anything that you would like to revisit, then please do so.

There will be instructions along the way as well, asking you to pause to take some time to complete an activity.

If you've managed to do all of those things, brilliant, if not, then do pause and collect anything that you need and press play when you're ready to resume.

So today's lesson, we're going to be calculating the area of non-rectilinear shapes.

So we're going to break this lesson down into looking at area measurement, area of non-rectilinear shapes and independent task and we will finish with a quiz.

Things you'll need for this lesson, you'll need a pencil to write with, a ruler and some paper as well.

So if you don't have those materials now, please pause the video, collect those things and press play to resume.

Right, we'll start with a warmup then.

So are these statements true or false? One centimetre square is equal to 1000 square millimetres.

Is that true or false? Second question, one square metre, is that equal to 1000 square centimetres? Yes or no.

Pause the video, think about your answers and press play to continue.

So, in fact, both of these statements are false.

If we look at each one in turn, you'll see that one square centimetre is equal to 10 millimetres by 10 millimetres.

And so it's equal to 100 square millimetres not 1000.

Similarly, one square metre is equal to 100 centimetres by 100 centimetres.

And that therefore is equal to 10,000 square centimetres not 1000.

So here we have the term non-rectilinear.

And what that means is, it's a shape that's not made up entirely of vertices with right angles like rectangles and squares.

So you'll see in these examples, there's very few right angles used and therefore we can describe these shapes as non-rectilinear.

So how are we going to work out the areas for each of these shapes? Well, in these examples, we have a square background and we can use that to help us.

So have a look at each of these four shapes and determine whether you can roughly estimate or exactly calculate the areas of each one, based on the information provided behind the shape.

Have a think, press pause, and then play when you're ready to continue.

Well, let's look at this first shape.

Here we have five squares and I can mark some of them here.

One there, two, three, four, and one in the centre, and then we have four half squares, one here, one here, one here and one here, okay? So if we add all that up, we have four halves, which is two, two wholes, five plus two is seven.

So the area of this shape is seven square centimetres.

Now the second shape, well, as a possible strategy, we could box it in.

So to box it in, we're going to create this rectangle shape around our shape so that it's touching as many sides as we can, okay? And this allows us to calculate the area of the rectangle and then subtract the area of each triangle like this one here, okay? So this rectangle would be one, two, three, four, five across and one, two, three, four down.

So that's five times four, which is 20 square centimetres, okay? But we need to take some of that off.

So if we look at each of these white triangles on the corners, you can see that these are made up of one full square and two half squares.

So each triangle has an area of two square centimetres.

So therefore we have a two, four, six there and eight there.

So 20 subtract eight is 12 square centimetres.

Let's look at the third example.

Again, we could box this in as a strategy and this would be four squares by four squares, which is going to give us 16 square centimetres.

And you can see that we're going directly across the centre here.

So this is half of the shape and therefore it's 16 divided by two, which is eight square centimetres.

Finally, we have 2 centimetres squares here, one, two, and we have four halves as these triangles here.

So that's going to be two more square centimetres in total.

So altogether, we have two full squares, four half squares which is four square centimetres.

So here we have some more non-rectilinear shapes and you can see they're a bit more difficult because the grid behind them doesn't line up nicely with the edges.

In this first example, you can see that we have two full squares shaded in, but also, we can just about make up another square using the top and bottom segments.

Similarly, you can see that these two sections pretty much make up another full square.

And then we have four of those.

So altogether, we can count the two full squares, the top and the bottom making a third square and then four of these additional side pieces and that's going to give us four, five, six, seven pieces in total.

So we can say this left-hand shape roughly has an estimate, has an area of seven square centimetres.

If we look at the right example, the oval, you can see there that there are five full shaded squares.

And then next to these, we have one, two, three, four, five, six squares that are almost entirely shaded in.

So that would take us up to 11 squares.

And then finally we have these.

And then finally we have these corner pieces here, one, two, three, four, and those would add up to roughly another square.

They look like they're just over a quarter each.

So altogether we have nine, 10, 11, 12 squares roughly.

So an estimate for this shape, it could be 12 square centimetres Time for an independent task.

Here are two shapes that don't fit nicely on a grid background.

Can you estimate the area of each one and decide which one is biggest? Pause the video, complete the task and press play when you're ready to resume.

Okay, let's try this together then.

If I have a look at this left-hand shape, you can see I have one full square there, another full square there, and this is almost a full square.

And then I have, this is almost a full square.

You can see that one there, and this one's nearly a full square as well, okay? So it's one, two, three, four, five.

If we take these little bits across the bottom, they will help make these numbers three, four and five become full squares.

So I think lastly, we could just about say, this could be a full square if we include this bit here and this bit here, whoop, a bit further down there, okay? So a good estimate would be around six square centimetres for the left-hand shape.

Moving over to the right-hand shape, we have one, two, three, four, let's call this five here, six, seven, eight, okay? Now we're going to ignore those little bits because they will help make up full squares from the ones that have a bit missing, like here or here.

So we can say this one as an estimate has an area of about eight square centimetres.

So which one is bigger? While we can see that the right-hand side shape has an area of roughly eight and the left-hand side is roughly six.

So the shape on the right is bigger.

So that brings us to the end of today's lesson, really well done on all the learning that you've done today.

It's fantastic.

And just before we finish, have a think about what the most important learning was for you in that lesson and maybe take some notes on that too.

Anyway, thank you so much for participating today.

Enjoy the rest of your day of learning and I'll see you again soon.