Lesson video

Hi, I'm Miss Kidd-Rossiter and I'm going to be taking today's lesson on area of triangles.

Before we get started, can you make sure that you're in a nice, quiet place, free from distractions that you've got something to write with and something to write on.

We're going to be drawing lots of shapes today.

So it'd be really helpful if you had a pencil and a ruler as well.

If you need to pause the video now to get anything sorted, then please do, if not, let's get going.

So for today's try this activity then, you've got four triangles on your screen, and it's your job to think about how many squares are shaded in each.

I'm really interested in the method that you use to do this.

So when you're working these out, if you can make a note of the method, that would be great as well.

So pause the video here and have a go at this task.

Excellent work.

I'm going to ask you what you got for each of them.

And I want you to tell me back to the screen, so, what did you get for the first one? Excellent, what did you get for the second one? Excellent, what did you get for the third one? Excellent, and what did you get for the fourth one? Excellent, you should have realised that all of them were nine squares.

Now I'm not actually too bothered about the result and about the answer.

What I'm more interested in is the method that you used to get them, so did you count squares? Did you count non-shaded squares and take it away from how many squares there were in total? Let's go through a couple of examples.

So for the pink one.

So the second one here I could have counted one, two, three, four, five, six, full squares.

And then I've got one, two, three, four, five, six, half squares.

So six half squares makeup how many full squares? Excellent, three.

So I've got six squares plus six half squares, which gives me nine squares in total.

Excellent, what about a different method? I think the counting squares method becomes trickier on the bottom two shapes because we've got parts of squares that are not halves.

And then we're having to look for which ones we can match up, how did you do it? Well, the other method that I thought about was I know that this shape here is a rectangle and from our previous work, I know that to find the area of a rectangle, I would do the base times the height or the width times the length you might've heard it said, so I can see that I've got three units going up and I've got six units going across.

So my rectangle would have an area of three multiplied by six, which would be 18 squares.

And I can see that my triangle is clearly half of my rectangle.

So that means that my triangle would be 18 divided by two, because that's what halving is.

It's dividing by two or sharing into two parts, which tells me that it's nine squares.

However you did it, I hope you managed to find an efficient method.

So well done on that.

All right, so here we are.

We've got two congruent.

Now congruent just means that they're the same size.

They've got the same angles, but one could be a reflection or a rotation of the other, and they can be joined along their longest side to form a rectangle.

So here is an example of how that could be done.

We need to see what other shapes could be formed if I joined the triangles along different sides.

And how could I use these shapes to find the area of the triangles? So pause the video now and have a think about that.

And I'd love to see some of your sketches.

Excellent, so there are six possibilities that you could have found here.

Here is the first one that we've already looked up.

Here's another option.

Here's a third option, here's a fourth option.

Here's a fifth option and here's the sixth option.

So we've got the six different shapes that we could have made by joining these triangles along their side lengths.

How can I use any one of these shapes to figure out the area of the triangle? Pause and think about that.

Excellent, if I know the full area of one of these shapes, then that means that the area of one triangle would be half of that shapes area, wouldn't it? So let's just have a look at this parallelogram here.

We know from our work previously that to work out the area of a parallelogram, we need the perpendicular height, which remember is the height that forms a right angle with the base.

So perpendicular height, and we also need the base don't we? So the area of a parallelogram is the perpendicular height times the base or the base times the perpendicular height, which we'll just write as base times height for now.

So how would we work out the area of the triangle then of one of the triangles? Excellent, it would be the base multiplied by the perpendicular height and then divided by two wouldn't it halved.

Excellent, so this statement here is really important.

I'd like you to pause the video now and write it down.

And then please also make note that the height is the perpendicular height.

Excellent, we're now going to apply your learning to the independent tasks.

So pause the video here, navigate to the independent task.

And when you're ready to go through some answers, resume the video, good luck.

Excellent work on that independent task, welldone.

Let's go through some answers.

So a rectangle is made of two congruent triangles, work out the area of one triangle.

Well, we know to work out the area of the rectangle, we would do five multiplied by 12, the base times, the perpendicular height, which gives us an area of 60 centimetres squared, and then find one triangle, we would half that.

So 60 centimetres squared divided by two gives us 30 centimetres squared, which is the area of one of our triangles.

Parallelograms are made of two congruent triangles in each case, work out the area of one of the triangles.

So for the first one, we know that the six centimetres is our base and we know that the eight centimetres is our perpendicular height.

So to work out the area of the parallelogram, we would do eight centimetres multiplied by six centimetres, which gives us 48 centimetres squared, but we want one of the triangles so we have to half that.

So 48 centimetres squared divided by two gives us 24 centimetres squared.

The second one, our base is our 11 millimetres and our perpendicular height is our 12 millimetres.

So that means that that area of our parallelogram will be 11 multiplied by 12, which gives us 132 millimetres squared.

And then triangle is going to be half of that.

So 132 millimetres squared divided by two gives us 66 millimetres squared, well done on those.

And then the third one, write an expression for the area of this triangle.

Well, if we had a parallelogram, it would be, A, because A is our base and H is our perpendicular height.

So the parallelogram would be the base multiplied by the height, which in this case, we've got letters haven't we, which is A multiplied by H and A multiplied by H, we can write as AH.

So that means that our triangle will be half of that.

So half times AH, we can write as half AH or you might have written it slightly differently as AH over two any of those are perfect, but you can see the answers that I've chosen to go with is that the area is equal to half multiplied by A multiplied by H.

Moving onto the explore task now then.

How many different expressions can you find for the area of the triangles in this diagram, pause the video now and have a go.

How did you do with that task? So we know don't we, that in each of these cases, that area of the triangle is going to be half area of the parallelogram.

So first of all, let's look at one over here.

So let's look at an example, parallelogram here.

So there's one on your screen now what's the base of this parallelogram? What's the base of this parallelogram? Excellent it's A, isn't it? And what's the perpendicular height? Tell me now, excellent it's P, isn't it? So the area of the parallelogram would be A multiplied by P or AP.

So that means that the area of the triangle would be half of that.

So the area would be half AP.

Now let us look at a parallelogram that we can find here on the bottom row.

So one that looks like this, I've drawn a bit of a neat one there on the screen before you, what is the height of this one? Can you tell me now? Excellent, it's R, isn't it? The perpendicular height is R, we know that because we're told that this here is R, and what's the base and this time, tell me now, excellent, it's C.

So that means the area of the parallelogram would be R multiplied by C, which we could write a CR.

And so we know the triangle would be half of that.

So it'd be half CR.

And then finally, we've got one that looks like this, which we could find here on our diagram.

So what is the height of this one? Excellent, it's Q isn't it? The height here is Q and what is the base? Excellent, it's B isn't it? So the area of our parallelogram would be B multiplied by Q or BQ.

And that means that the area of our triangle would be half of that.

So it will be half BQ, that was tricky.

So well done, if you managed to follow that, we've drawn loads of lovely shapes today.

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

That's it for today's lesson.

So thank you so much for all your hard work.

I hope you've enjoyed it.

Please don't forget to go and take the end of lesson quiz so that you can show me what you've learned and hopefully I'll see you again soon, bye.