Lesson video

Hello, and welcome to this final lesson on revisiting area.

In this lesson, we'll be looking at working out sidelines when given areas.

My name is Mr. Masego.

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

Okay, now that you've got those things, let's get on with today's lesson.

First try this activity, pause the video here and give this a go.

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

Well, give possible base and height lengths for a triangle with an area of 24.

What could we have? Well, we want to get an area of 24, and we're not to work out the area of a triangle.

It is base times height divided by two that gives us our area.

So our base times height has to be double 24.

'Cause the only half it will get 24.

So we could have had 12 by four to the base of 12 centimetres and a high to four centimetres.

Well that would give you 12 times four is 48 divided by two is 24.

What else could you have had, you could have had a triangle with eight by six.

So as long as you get 48 so that you can half it to get 24, you'd have been fine.

So for this trapezium, what would the a b and h length be to give us an area of 24? Well, how do you work out the area of a trapezium? Well we noticed a few lessons ago that the area of a trapezium can be given as a plus b times the height divided by two.

So sort of like the triangle look, we've got something times the height divided by two.

So a plus b times height, this has to be 48 because when you divide that by two you get 24.

So you need two numbers that will multiply to give you 48.

So we could have 12 and four and now a and b.

So we can say the height is four a and b have to add together to give you 12.

So any two numbers that add to give you 12.

So you could have had seven and five 'cause seven plus five.

Well, that gives you 12 times four is 48 divided by two that gives you 24.

Now the easiest one of the three was the rectangle.

And now in the rectangle, you could have read what? Just to get 24.

You could have had at 12 times two or you could have had eight times three or six times four.

So any two numbers are multiplied to give you 24.

Now what we're looking at today is we're going to be working on sidelines.

We'll have given an area and one other sideline.

So here's the rectangle.

And this rectangle has an area of 18 centimetres squared and we know the base is six.

So what is the height of rectangle? Well, we know to work up the area rectangle is base times height.

We know the basis six the area is 18.

So 18 equal six times something and we know about would be three centimetres.

We know that six multiply by three gives us 18.

You could have done 18 divided by six to find out about the height was equal to three centimetres.

Now rectangles are the easiest ones to do, because we're just looking for a factor pair.

That makes our area.

Now, what about triangles? Now in this triangle, we know that the base is four centimetres and we know that the area is 18 centimetres.

How do you work out the area of a triangle? Good, it's base times height divided by two.

So what would the height of this triangle be? What do the base and height have to multiply two? So that area is 18.

Well, we're going to have to divide that by two.

So something divided by two, gives you 18 and that would be? Good 36 cause double 18 is 36.

So we know that the base in the heights have to base times the height have to multiply to give you 36.

So four time something gives you 36.

So the height will be good nine.

So the height would be nine centimetres because four times nine is 36.

So just look for factor pair that gives us 36.

And we know that 36 divided by two is 18.

Now here's a trapezium and we've been given a as seven b as five and the area is 30 and we have to workout what the height is.

Now how would you do this? Remember the formula to work out the area of a trapezium, that a plus b times the height divided by how would you work out the height? Pause the video here and give this a go.

Okay, now that you've tried this, let's see what you're going to come up with.

What does this have to multiply to? Good that has to multiply to 60.

Why does it have to multiply to 60? Because at the end we're going to divide it by two to get to our area of 30.

So it's the same as when we have a triangle.

So the formula to work out the area of a triangle and the trapezium is very similar.

On the triangle we just have base times height, but on the trapezium is that a plus b So you add the two parallel sides and then you multiply by the height and then divide by two.

But that's the numerator of that fraction.

So that part of the fraction has to be double the area.

'Cause when you divided, you will get what the area was.

So you need two numbers multiply to give you 60.

Well, we already know a plus b, a plus b is good 12.

So we know that 12 multiplied by the height has to give us 60.

So 12 times something gives us 60.

So the height has to be good, the height has to be five centimetres.

Okay, here's an independent task for you to try.

These four shapes have the same area.

So work out the Heights of the other three shapes? Pause the video here and give this a go.

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

Well, you should have worked out the area of the rectangle, but is 40 centimetres squared, now full the triangle.

Remember that is base times height divided by two.

So the base times the height, well that has to equal 80 because 80 divided by two is 40.

So eight times the height gives you 80.

So the higher it has to be 10 centimetres.

Now the area of a parallelogram.

Well that is just base times height.

Well, 10 times the height is 40.

The height is four centimetres.

The area for trapezium remember that is a plus b times the height divided by two.

Well, a plus b that is 10 add 16 10 at six times, the height divided by two.

Now that will be 16 times the height divided by two.

That's 16 times height.

What does that have to equal well 16 times of highest this has to 80 because 80 divided by two is 40.

So 16 times the height is 80.

So the height has to be five centimetres.

Now here's an explore task.

Workout the the length a, b and h for four trapeziums that have consecutive areas and what is consecutive mean? Consecutive means like three, four, five, six.

So the areas have to be increasing by one each time.

So what could be the values of a, b and h b for four trapeziums that have consecutive areas? Pause the video here and give that a go.

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

Well, let's use the numbers that I gave to have an area of three.

We know that a plus b times h has to be six because a plus b times the height divided by two is area.

So do you have an area of three? a plus b times h has to be six because six divided by two.

That gives you three.

So we could have, what two numbers multiply to give you six? Well, three and two.

So you could have the base as two a as one and the height as two, because two plus one is three times two, six divided by two that's three.

So that gives an area to the area of this is three.

Now we got an area four well, a plus b times height has to be eight so we could do two.

So what we could do three, one and two, 'cause three plus one is four times two is eight and then divided by two that's four what about the next one.

Well, we could do a base of four an a of one and a high of two, 'cause four plus one was five times two is 10 divided by two is okay.

What about the next one? We could do five, one and two, because five plus one is six times two is 12 divide.

Okay.

What are you noticing? Whoa, we can see that the length a is staying the same all the way through.

The length b, what's happening to that? Well, that's just increasing by one throughout.

So starting at the huh, but what else can you see? Well, here when our height is two our areas are just what's a plus b when our height is two our areas are just a plus b.

Cool, well in this sequence, what would the 20th area be? what would be the side lengths for the 20th trapezium? Well, how can you figure that out? Well what can we see if the area is three b is two the areas four b is three, the areas five b is four.

So if the area is 20 well in this sequence, b would be 19 and a would be one and h would be two 'cause 19 plus one is 20 times two 40 divide by two 20.

When you height is two your area is always just a plus b for your trapezium.

Now some of you may have just picked different numbers for this.

So you could have done a height of three.

Like what did you notice when your height was three? What do you notice when your height is four? What do you notice when your height is five? Now if you want to share any of the discoveries that you made, ask your parent or carer to share what content to tagging at OakNational and #LearnOak Now, this was the last lesson in reviewing area.

So look forward to any of the work that you sent in.

Thank you very much for taking part.

I will see you again next time.