Lesson video

Hello and welcome to this lesson on "Revisiting Area." Today we'll be looking at rectangles and triangles.

My name is Mr. Maseko.

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

Now, if you have those things let's get on with today's lesson.

First try this activity, what other calculations can you write for these diagrams? Yasmin says she can write six times four, add three times four for this first diagram.

So pause the video here and give this a go.

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

Here are some calculations that you could have come up with.

For this first one, you could have had six add three times four, which can just be written as nine times four.

For that second array, you could have had one time six, add three times four, which can simply be written as six add three times four.

So what did these calculations actually represent? Well, you'll find that these calculations represent that areas of these arrays.

Well, how do we know this? Well, if we just focus on this first calculation, six times four, so six multiplied by four is the area of that first rectangle and three times four is the area of that second rectangle.

That's the same thing for this calculation.

Well, one time six, well that's the area of that first rectangle, and three times four is the area of the second rectangle.

And that's what we're looking at today, we're looking at areas of rectangles and triangles.

Now, these are shapes drawn on the unit grid.

Now, what does that mean? That each square is worth one units.

So these shapes are drawn to scale.

So by counting squares, what is the area of these two shapes? What do you notice? Pause the video here and give that a go.

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

Well, you should have noticed that the area of that rectangle is 12 unit squares, so 12 unit squares.

And that area of that triangle, if you count them we go one, two, three, four, five, six, seven, eight, and then you have nine, 10, 11, 12, and that's also 12 units squared.

Those two shapes have the same area.

Well, let's look at the side lengths.

Well, the base of this rectangle is four units.

So it's four units and the height is three units.

So it goes up to three and the base is four.

Whereas the base of this triangle is four units and the height is six units, but they have the same area.

Why is that? We already know to work on the area of the rectangle, we do base multiplied by height, 'cause four times three gives us our 12 units squares, 'cause there's 12 unit squares in that rectangle.

So how do we work out the area of a triangle.

Well, I can hear you say it, keep that thought.

Without counting squares, work out the area of this second triangle.

So using that thought that you just came up with, how to work up an area of a triangle without counting squares, work out the area of that second triangle.

Pause the video here and give that a go.

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

Well, we already that this area is 12 units squares, this one is also 12 units squares.

And then this one, well, how did you work that out? This one has, if you look, it has a base of four units and it has a height of six units, and the area was 12 units squares.

How do you work it out? Well, you can see that the area of a triangle, so the area of a triangle, you notice is the base multiplied by the height divided by two.

So what do you notice about the base and height lengths of rectangles and triangles that have the same area? What do you notice? Good, you can see that one of the lengths is the same and now for the triangles, the other length is double the length on the equivalent rectangle.

Now, why is this? Why is it that for other the triangle, the other line has to be doubled to make the area the same.

Good, because at the end to find the area of the triangle, we have to divide the base multiply by height by two.

Now, why do we divide the base multiply by the height by two? Well, if you notice, a triangle is just half of the rectangle.

So we've taken a rectangle and we've split it in half.

That is why when we find the area of the triangle, we do the base multiply by the height, and then we divide that by two.

Now has an independent task, on the grid below each rectangle, draw a triangle with the same area.

Pause the video here and give this a go.

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

Well, if you look, what's the area that first rectangle? Well, it has one, two, three, four, five, six, so that is six unit squares.

Now, why am I saying six unit squares? Well, that's because we don't know whether this is a centimetre or a millimetre grid or a metre grid, but we know that it's to scale.

So this can be any units.

So it could be six centimetres squared, it could be six millimetres.

Now, I could have a triangle with a base of two.

Now if my base is two, what would my height be? Only one of lengths will be double, so my height would be six.

Now triangle has the same area as a triangle, 'cause base times height, two times six divided by two, two times six is 12, divided by two, that gives you six unit squared.

Same thing for that second one, well, the area of this is six times two, which is 12 units squared.

So I could have one with the base of four at a height of six, and that'll give me an area of 12 units squared.

Now, for this second one is five by three, so that's got an area of 15 units squared.

So we could have a base of six and a height of five.

We've got a height of five and a base of six, that is an area of 15 units squared.

Now for this last one, we have a base of eight and a height of four, so that's 32.

So I could have a base of eight and a height of eight and that would be my triangle with the equivalent area.

One of the lengths of my triangle has to be double one of the lengths on my rectangle to make an equivalent triangle.

Now really well done if you got all of these.

Now, here are some parallelograms drawn on a unit grid.

Draw some rectangles with the same area, what do you notice? How would you work out the area of a parallelogram without counting squares? Pause the video here and give that a go.

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

Well, by counting squares, you should have noticed that the area of that first parallelogram, that was 20 units squared.

If we want a rectangle with an area of 20, well, that is a four by five rectangle.

That second one, that was 16 unit squared.

Now, a rectangle that is you can have a two by eight rectangle.

Now you've got a four by three parallelogram.

Now there's a reason I really like about this time.

I'm not going to count those squares.

That parallelogram has an area of 12 units squared.

So you could have had a four by three rectangle.

Now why did I do that? How did I know that parallelogram had an area of 12 without counting both squares? Well, you could just say I made the question so I know the answers, but how else? I'll give you a clue the last one as well.

A three by five, this one you should have counted as 15 units squared, which has the same as a three by five rectangle.

Ah, what do you notice? Well, you should've noticed that the area of your parallelograms is just the base multiplied by the height.

And if you notice, the base and the height are perpendicular to each other.

A parallelogram it's just a rectangle.

So if you look, we can actually prove that a parallelogram is just a rectangle.

So if you take the end of your parallelogram, so if we just cut this end off and we take it and we paste it over here, look at what shape you have.

That inside there, that is just a rectangle and it's what? It's that five by four rectangle.

If I take that off, see, you've got up five by four, that parallelogram is just a rectangle that has been squished a bit.

So I really hope that you've learned something in today's lesson something about working out the equivalent areas for triangles, rectangles and not even parallelograms. If you want to share some of your work, ask your parents or carer to share your work on Twitter tagging @OakNational and #LearnwithOak.

Thank you for taking part in today's lesson.