Lesson video

Hi, I'm Mr Chan, and in this lesson, we're going to learn about the area of rectangles, parallelograms and triangles.

Let's recap finding the area of rectangles, parallelograms and triangles.

I've got those three shapes drawn out in front of me here, so let's calculate the are of each shape one at a time.

Let's look at the rectangle.

Now, to work out the area of a rectangle, we must multiply the length with the width, so we've got 12cm and 20mm.

So we would multiply those two together, however, I do notice that the units aren't the same here, one's measured in centimetres, and another is measured in millimetres.

So it's important that we only deal with consistent units while we're working with area, so let's be careful with that, and let's treat both as centimetres to start with.

So I'm going to write the 20mm as 2cm.

So, we would multiply those two together, 12 multiplied by 2 gives me an area of 24cm squared.

Now if we were to multiply those two length and width together as millimetres, this is what my calculation would look like.

The 12cm would become 120mm, multiply that by 20mm and in terms of millimetres squared, I would get an answer 2400mm squared.

Let's look at the parallelogram.

Now, to work out the are of a parallelogram, we multiply the base with the height, base times height.

Now, it's important when we're working out the area of parallelogram the height we use is the perpendicular height, which is the height at a right angle to the base.

So that would be the 5m in this diagram here.

Again, I notice that there's a 720cm that isn't consistent with the metres, but we're not going to be using that length in terms of working out the area, so we can ignore that.

The base is 9m, so I'd multiply these two together, 9m multiplied by 5m, that gives me an area of 45m squared.

Moving on to the triangle.

The area of a triangle is half multiplied by the base, multiplied by the height, half times base times height.

So again, in terms of working out the height, we need the perpendicular height, and that's the height at a right angle to the base.

So that would be the 6cm here.

So the two lengths I would be using would be the 14cm base and the 6cm perpendicular height.

There's also a 130mm shown there, and I won't be using that length to work out the area, so I can ignore that.

So the area calculation becomes half times 14 times 6, that gives me an area of half times 84, and a final area of 42cm squared.

Here's a question for you to try.

Pause the video to complete the task, resume the video once you're finished.

Here are the answers.

So in this question we must work out the area of rectangles.

And we've got two rectangles there, where we work out the area by multiplying the length by the width.

Now, it's important the we do use the correct units and we can see from the first question and indeed the second question that units aren't the same.

So in the first part I would change the 300cm into metres, and multiply the 4.

5 by 3 to get an answer of 13.

5.

And in part B, we've got 5km and 12,000m.

In that question I would probably change the 12,000m into kilometres, so it would be 5 multiplied by 12km, to get an answer of 60km squared.

Here's a question for you to try.

Pause the video to complete the task, resume the video once you're finished.

In this question, Eva's working out the area of a parallelogram.

Now, I've checked the units, all the units are centimetres, so that's fine.

The area of parallelogram is base multiplied by perpendicular height, and I think that's what Eva's done wrong.

She's multiplied the 10, which is the sloped height with the 20, which is the base, so her mistake is that she's not multiplied the base with the perpendicular height, and if she did do that, she would get the answer 160cm squared.

Here are some more questions for you to try.

Pause the video to complete the task, resume the video once you're finished.

Here are the answers.

So in question three, it's asking you to find the length of AB.

You're given the area of the parallelogram.

So the area of the parallelogram is 54m squared.

You're given the perpendicular height of 6m.

So we know that the area of a parallelogram is base multiplied by the height, so we just need to figure out what we multiply by 6 to get the answer of 54m squared.

So we could do a division calculation to work that out, but I do know that 9 multiplied by 6 gives me 54, so the base AB must be 9m.

In question four, we need to work out the area of the triangle and decide which answer it is.

So the area of a triangle is half multiplied by the base, multiplied by the height.

In this rotated triangle, the base I'm going to take as 10, because that gives me a perpendicular height of 7.

10 multiplied by 7 gives me 70, and if I half that answer, I get 35cm squared.

Here's another question you can try.

Pause the video to complete the task, resume the video once you're finished.

Here's the answer.

So in this question we're given all three types of shapes.

We've got a triangle, a parallelogram and a rectangle.

Now, we've got to be careful with a couple of those shapes, the triangle and the parallelogram in particular, because it's given me some side lengths that I need to ignore.

So remember a triangle we only need the base and the perpendicular height.

The parallelogram, again we only need the base and the perpendicular height in order to work out the area.

So once we've used the correct formulas, we work out the area, and indeed we find the rectangle has the greatest area in this question.

That's all for this lesson.

Thanks for watching.