Lesson video

Hi, I'm Miss Kidd-Rossiter, and I'm going to be taking today's lesson on area of parallelograms. It's going to build on all the work that we've done so far on area and perimeter of 2D shapes.

So hopefully you're really excited to get going.

Before we start, can you make sure that you've got no distractions; you're in a nice quiet place, if you're able to be, and that you've got something to write with and something to write on.

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 to work out, what is the area of each shaded shape? So pause the video now and have a go at that.

Excellent; there are loads of strategies here that you could have used.

You could have tried pairing up part squares to make full squares.

You could have worked out the area of each of the unshaded parts and taken it away from the area of the full rectangle.

So really good work, whatever you did.

Here are your answers.

So for the first one, it's 20 squares and for the second one, it's 15 squares.

Now these two shapes are what we call parallelograms. And we're going to look now at how we would work out the area of a parallelogram.

So a parallelogram can be cut up and rearranged to make a rectangle.

So if you look at the diagram there that's on your screen, you can see that we've cut off the shaded part of the parallelogram here, and we're going to move that.

So we remove that, and when we move it to the other end of the parallelogram, you'll see that we form a rectangle, where we've got a width here and a height here.

So will this always work? And then, what lengths would you need to know in order to find the area of the parallelogram? Pause the video now and have a think about this.

Okay, let's look at another couple of examples together.

So we've got two parallelograms on the screen.

We're cutting them in different places this time.

So the first one we're cutting here.

Let's see if that will form a rectangle.

If we remove that part, yes it does, doesn't it? And here, if we remove this part here, does it form a rectangle? Yes, it does.

So if we were working out the area of these rectangles, what would we do? Excellent; we would do the base of the rectangle multiplied by the height, wouldn't we? And that would be the same for this one.

I'm just going to use the letter H for height and B for base from now on.

So here we would do the height multiplied by the base to find the area, wouldn't we? So let's see if that still works when it's a parallelogram.

So we would need to have the base, which is this part here.

And then the height, which is from the top to the bottom.

And this is the perpendicular height.

So it forms of right angle with the base.

And that would be the same for this one as well.

We would have the base here multiplied by the perpendicular height.

So I want you to write this down, please.

Area of a parallelogram is the base multiplied by the perpendicular height.

So sometimes they might give us the slant height to try and confuse us, but we know that it's the base multiplied by the perpendicular height.

Excellent work.

So pause the video now and write that down if you haven't.

Excellent! So you're now going to apply your learning to the independent task.

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 part.

Let's go through some answers.

So the first one here has got a base of four units and a perpendicular height of four units.

So that means the area is four multiplied by four, which is 16 squares.

Second one, we've got a base of five units and a height of two units.

Remember it's the perpendicular height because it forms a right angle here.

And that means that the area is five multiplied by two, which is 10 squares.

Work out the area of this parallelogram then.

So this is our base and this is our perpendicular height.

So we're going to do four centimetres multiplied by six centimetres, which gives us an area of 24 centimetres squared.

And just a quick note.

Remember not to use the slant height, which is 10.

So we don't use that one when we're working out the area.

A parallelogram with area 126 centimetres squared sits behind three identical rectangles.

What is the area of each rectangle? Well, you can see it there on the screen.

126 divided by three is 42 centimetres because we know that the parallelogram has got the same base as each of these rectangles.

And together of the three rectangles has got the same height.

So its area has to be three times the area of one rectangle.

So to work out one rectangle, we would do 126 divided by three, which gives us 42 centimetres squared.

Moving on to the explorer task now then.

Explain how you know that the area of the six rectangles is equivalent to the area of the parallelogram.

And then, can you write an expression for the area of the parallelogram? Pause the video now and have a go at this task.

Excellent; so the first thing we need to know is that the rectangles have the same base as the parallelogram.

And then together, one, two, three, four, five, six rectangles have the same height.

Remember it's the perpendicular height as the parallelogram.

So that means the six rectangles all together have the same area as a larger rectangle that would have the same base and the same perpendicular height.

So that means that it's equivalent to the parallelogram.

In fact, it doesn't matter how these rectangles are stacked on top of each other.

It could be in any way, sort of like this.

So long as they're stacked one on top of the other in a better way than I've drawn it, then the area will always be the same.

So let's write an expression for the area then.

Well, first of all, we need to know the area of one of the rectangles.

So we know that the area of one of the rectangles will be A multiplied by B, which we can write as AB.

And then we know that the parallelogram has the same area as six of these rectangles.

So we're doing six multiplied by AB, which we can write as 6AB.

Excellent work, well done.

That's the end of today's lesson.

So thank you so much for all your hard work.

I hope you've learned loads about area of parallelograms. Please don't forget to go and take the end-of-lesson quiz and so you can show me what you've learned.

Hopefully I'll see you again soon; bye.