Lesson video

Hello, and welcome to this lesson.

My name is, Mr. Maseko.

In this lesson we'll be looking at compound shapes, and their areas.

Before you start this lesson make sure you have a pen, or a pencil and something to write on.

Okay? Now that you have those things, let's get on with today's lesson.

First, try this activity.

This is a shape drawn on a unit grid.

And on these grids here, I want you to draw a triangle and a rectangle that has the same area as the shape here.

Pause the video here, and give this a go.

Okay.

Now let him tried best.

Let's see what you come up with.

Well, you should have realised that this shape has an area of twenty four units squared.

Because you counted the squares in that you've got to twenty four.

So you want a rectangle with an area of twenty four.

So think of all effect to pads of twenty four.

You can have a base or four, and a height of six.

or eight and three, or 12 by two.

I'm just going to go four and six.

So we can have a base of four, and a height of.

six.

And that's a rectangle with an area of twenty four.

So four, five, six.

Now we want a triangle with that same area, the how to work out the area of a triangle.

Well, remember it is base times height divided by two.

So our base for our triangle it'd be eight, then our height that can be six, because we know if we do eight times six divided by two, that would give us twenty four.

So in today's lesson, we are looking at working out the areas of compound shapes.

Now compound shapes, are shapes made from two or more shapes put together.

Now without a unit grid, how would we work out the area of this shape? If we weren't, if we were just given the sidelines, well, what can you see in this compound shape? Well, you can see that this has, if I do this, we have a triangle in that, and we have two rectangles.

So, we split this shape into three separate components.

So you can see that this is a compound shape that's made from one triangle and two rectangles.

Now am going to label this as one, two, and the triangle can be labelled as three.

Now, rectangle one, what's the area of that rectangle? Well, it has a base of four, and a height of four.

So four times four, that is sixteen centimetres squared, and then rectangle two.

Well, that has a height of three.

What is its baseline? Well we know that from there, to there is four centimetres, while the whole length is six.

So that missing length is two centimetres.

So that second rectangle is three by two, which is six centimetres squared.

And now what about the triangle? Well, for the triangle, we have a base of two, a height.

What's the height.

Well, we've got three centimetres.

We'll go one extra centimetre to get to four, and another centimetre.

So that triangle is two by two.

It's two times two, because the triangle, we divide by two.

Why do you divide by two for triangle? Because the triangle is half a rectangle.

SO it's two times two divided by two, which is two centimetres squared.

So the total area of that shape.

So the total, area.

would be, you add all of those together, which is twenty four centimetres squared just by splitting our shape into its component parts.

We were able to work out the area of the shape.

Look at this trapezium, now a trapezium is a quadrilateral What does quadrilateral mean? It's a shape that has four sides, and it has a pair of parallel sides.

So this is what a trapezium is.

How many different ways can you come up with to work out the area of this trapezium.

Now I want you to try this on your own first, before I give you a clue, pause the video here, and give this a go.

Okay? Now that you've tried this, let's see what you could have come up with.

And you could have say chopped this trapezium here.

Say you cit that off.

What you're left with is this.

And then that piece that you've chopped off the end.

Well, what can we do with it? We can take that piece, and then twist it round, and edit onto this side so that you end up with this rectangle.

And it's a rectangle with a a height five.

and a base of what's the base going to be? If you look that's our base we've chopped off the end, here.

So what was that length that we chopped off? Well, that length there is two centimetres.

Well, how do I know? Because, if you look at this, the middle is worth four centimetres, and on either side could going to make to eight centimetres on either side, we have two centimetres.

So that baseline is, six centimetres.

So, to work out the area of this trapezium with five by six, which gives us thirty centimetres squared.

Okay.

So that's one way we could have done this, and we get an area of thirty centimetres squared when we do this, but, we sort of just moved chopped a bit off, and moved into the other side, and then twisted it to make this a rectangle.

But how do we know that this actually works? Because, I said that this two lines were equal.

So they were both two and two, but does this work? Now, when we do stuff like this and that.

If we can do multiple different ways, and get the same answer then we know that it's true.

Now let's try it a different way.

Another way you could have come up with this, I'm going to delete all of this, but I'll leave our target area.

So we know that we're looking for an area of thirty centimetres squared That's what we worked out with the first method.

Another way you could have done this, is you could have just replicated that trapezium, and now what do you have? Well, if you look at this shape that we have now, you make, so we've now made a parallelogram, and we know how to work out the area of parallelograms, and the area of parallelograms, it's just base times height.

Well, what is the base of this parallelogram? We've got a length of eight, and then it could a trapezium, and flipped it over this length there is four, So eight by four like, it was a base of twelve centimetres and the height or the height is so five, centimetres so what we have is, that parallelogram has an area of twelve, times five, which gives us sixty centimetres squared, but we used two of our trapeziums to make that parallelogram.

So if we do sixty divided by two, we get an area of thirty centimetres squared.

Look, we've done it a different way.

And we've got the same area.

First, we made into a rectangle and I got an area of what?Thirty, we made it into a parallelogram by joining up two of our trapeziums. And we've got an area of 30 for one of our trapeziums, now what other ways could you have done this thinking about compound shapes.

I've show you two ways.

Well, again, let's delete all this.

Another way you could have done this is, you can see that this trapezium is made from, a rectangle in the middle, and two identical triangles on either side.

So that rectangle is four by five.

This triangles are five by two.

So the rectangle is worth twenty centimetres squared cause five times four the triangle, five times two divided by two, that is five centimetres squared.

And that's also five centimetres squared.

When you add all those together, 20 at five, at five, you get an area of thirty centimetres squared.

And we've worked out the area of this trapezium ,three different ways.

Now there are many other ways that you could have tried to work out the area of the trapezium.

Now, for this independent task for each of these trapeziums I want you to draw two compound shapes with the same area.

So pause the video here, and give that a go.

Okay.

Now that you've tried this, let's see what you've come up with.

Well, the area of that first trapezium was twenty eight centimetres squared.

Now you could have worked it out anyway, but I showed you three different ways.

You could have worked them out the area of that second trapezium.

Well that's one is twenty centimetres squared.

Now you are to draw four different compound shapes.

Two of them with an area of twenty eight, and two of them with an area of twenty.

Now, you could have decided to combine any shapes that you wanted, but as long as the areas were twenty eight, now on a grid, it's nice and easy.

You just have for the first shape, you have to cover twenty eight squares.

The second shape you have to cover 20 squares.

So if you count the number of squares in your shapes, the shape that you made, these ones have to have twenty squares in them.

And these ones have to have twenty eight squares in them, now for this explore task.

Can you use one of the ways that we figured out of working out that area of a, trapezium to show that the formula to work out the area of the trapezium is a plus b multiplied by the height, divided by two, pause the video here' and give that a go.

Okay.

Now that you've tried this, let's see what you could have come up with.

We know that I have to divide by two at the end.

So which one of our methods did we have to divide by two at the end for, well, we took our trapezium, and made it into a parallelogram.

By twisting it round, and joining at the end.

So this length is a that is b.

And we know about the heights is h.

Now that parallelogram that we've just made.

What's the area of that parallelogram? What we know the baseline of that parallelogram is a plus b, and the height is h multiplied by the Heights.

We know we want the area of our trapezium and our trapezium is made from two, and our trapezium is half of this parallelogram.

So we know about you're going to what? Divide by two at the end.

Now this is one way you could have shown this.

Now you could have used the other methods to also do this, but turning it into a parallelogram was the easiest way to do this.

Now that's it for today's lesson.

Thank you so much for joining in.

And I hope you learnt a lot about different ways we can work out the areas of compound shapes.

I was splitting them, or turning them into other shapes that we know how to work up the areas off.

I will see you again, next time.

Bye for now.