Lesson video

Hi year six.

Welcome to our fifth lesson in the decimals and measures topic, today we'll be calculating the area of parallelograms and triangles.

All you'll need is a pencil and piece of paper.

Pause your video now and get your equipment together.

So we will be calculating the area of parallelograms and triangles.

We'll start with knowledge quiz to test your learning from our previous lesson, then we'll look at the area of a triangle and then a parallelogram before you do some independent work and then a final quiz to test all of your learning.

So pause the video now to complete your initial knowledge quiz and click restart once you're finished.

So we'll start by thinking about calculating the area of a triangle.

The diagram shows a rectangle divided in half and it is divided into two right angle triangles.

So what do you notice about the diagram? What you should have noticed is that a rectangle is therefore made up of two triangles.

Now we've got some measurements associated with these triangles now.

So the right-angle triangle has sides of three centimetres, four centimetres and five centimetres.

It's perimeter is 12 centimetres three plus four is seven plus five is 12.

But what about this area? If you know that a rectangle is made up of two triangles, how do you think we can calculate the area? Pause and take a moment to think about this.

So we know that the triangle is half the area of the rectangle.

So the area of the rectangle is three times four, which is 12 centimetre squared.

Then the area of the triangle is half of that.

So the area of the triangle is six centimetres squared.

Let's explore this a bit further.

So here I have another triangle.

So if I multiply the width and the height of the triangle, then I get 18 centimetres squared as its area, but that's not finding the area of the triangle, but it's finding the area of the rectangle that it's within.

So multiplying by three by six, I've actually found the area of this entire rectangle.

Remember that the triangle is only half of the area of the rectangle.

So once we have the area of the full rectangle, we can half it to find the area of the triangle.

Therefore, 18 divided by two is equal to nine centimetre squared, and that's the area of our triangle.

So now we have a formula, the area of any triangle be calculated using this formula width times, height divided by two.

But we need to be really clear on what we mean by the height of a triangle.

So the height is calculated by drawing a perpendicular line from the base of the triangle to the upper most point of the triangle.

So you can see that these lines are perpendicular, which means that they create a right angle.

Sometimes you'll be given the measurements of the side lengths of the triangle, but you need to make sure that it's the correct one to calculate the area and I'll show you what that means on this next slide.

So here we've been given an extra measurement that the side is five centimetres, but we need to remember to use the actual height.

Remember that height is calculated by drawing this perpendicular line from the base to the upper most point of the triangle.

So we can ignore this five centimetres.

We're actually only interested in the face measurement and the height measurement.

So we can calculate the area of this triangle by multiplying six and four, and then dividing our answer by two, six times four is 24 divided by two is equal to 12 centimetres squared.

Remember that the triangle is half of the area for rectangle.

Therefore we must always remember to divide by two.

So now pause the video and calculate the area of each triangle using this formula.

So for the first one, you will have multiplied 21 by 19 and then divided your answer by two 21 multiply by 19 is 399 divided by two gives this triangle an area of 199.

5 millimetres squared.

Don't forget your units.

So for the next one, you were given an extra measurement that you didn't need.

You needed to use the perpendicular height.

So you were multiplying three by 0.

4 and then dividing that by two.

So that's 10.

2 divided by two is equal to 5.

1 centimetres squared.

And then your final one 50 multiplied by 15 divided by two, which is 750 divided by two is equal to 375 millimetres squared.

Super straight forward, always make sure you use the formula and don't forget, you have to divide your answer by two.

So now we're going to move on to calculating the area of a parallelogram.

Here we have a picture of a parallelogram, which is nine centimetres wide and five centimetres tall.

Now, if I take off a section of the parallelogram here and move it over to the other side here, you can see that it becomes a rectangle.

So we can use the same formula to calculate the area of a parallelogram as we do to calculate a rectangle.

So calculating the area of a rectangle is simply width by perpendicular height, width multiplied by perpendicular height.

So again, we mean a perpendicular line from the base to the top where we have a right angle.

So this extra measurement that's given here is not the one that we would use to calculate the area.

So that's where you may be may slip up.

You need to be really careful there.

So for this one, we would multiply seven by 2.

7, which remember me multiply decimals.

In our previous lesson, we did seven multiplied by 27 and divided the answer by 10, which is equal.

Or we don't need that extra bracket there, sorry, which is equal to 18.

9 centimetre squared.

So parallelograms is super straightforward, the same formula for calculating the area of a rectangle.

So now I'd like you to pause the video and calculate the area of each parallelogram using the formula.

So for the first one you were using this perpendicular height.

So 5.

6 multiplied by 4.

2 and remembering how we multiply our decimals, that will be 56 multiplied by 42 divided by 100 is equal to 23.

52 centimetres squared.

And then on rhombus, this is 3.

2 multiply by 3.

2, which is 32 times 32 divided by 100, which is equal to 10.

24 centimetres squared.

Now it's time for some independent learning.

So pause the video and complete the task and then click restart once you're finished.

So for question one, you had to calculate the area of each triangle and each parallelogram.

The first one, remember that the triangle is length times height divided by two, 120 times 90 divided by two is equal to 5,400 millimetres squared.

And then again, another another triangle 32 multiply by 11 divided by two is equal to 176 centimetre squared.

And then our parallelogram is the same calculations for the area of a rectangle 14.

5 multiplied by nine is equal to 130.

5 centimetres squared.

And finally, 88 multiplied by 23 is equal to 2024 centimetres squared.

For your next question, Elizabete was calculating the area of the parallelogram.

She said, I measured the two sides and found that they were seven centimetres and two centimetres.

Therefore the area is 14 centimetres squared.

Explain why she is incorrect.

So Elizabete thing is not to used the perpendicular height.

She sees the lengths of the sides.

So what she should actually have done is seven multiplied by 1.

6 centimetres and got 11.

2 centimetres squared, Question three Ronaldo had drawn a design of a fish easing six congruent equal lateral triangles here, two identical right angle triangles and two identical parallelograms. And we were asked to find the area of the design in total.

So beginning with the parallelograms to calculate the area of the parallelogram, that was eight multiplied by 3.

5.

So for each parallelogram, the area was 28 centimetres squared, moving onto the equal lateral triangles.

They had a base of four centimetres I'll do on this one here, a base of four centimetres and a perpendicular height of 3.

5 centimetres.

So to calculate the area of the equal lateral triangle, it was four multiplied by 3.

5 divided by two, and that is equal to seven centimetre squared.

So each equal lateral triangle had an area, a seven centimetre squared.

And I like to annotate it onto my diagram to help me out later on to the right angle triangles.

They had a perpendicular height of 5.

5 centimetres and their base was four centimetres.

So that is 5.

5 multiplied by four, and then divided by two, which is equal to 11 centimetre squared.

So each of them I'll annotate it on here, had an area of 11 centimetre squared.

So then all we needed to do was to add all of these areas together.

And the total area was 120 centimetres squared.

So for this question, we have a trapezium made of three isosceles triangles and a parallelogram.

The base of each triangle is 12 millimetres in measurement.

So I can add that onto my diagram and now cut calculate the area of each triangle by multiplying the base 12 by its perpendicular height, which is 27.

And then dividing that by two, which is 162 millimetres squared.

I have three triangles.

So the area of the three triangles is 486 millimetres squared.

Then I'm looking at the parallelogram and I can see that it has a perpendicular height of 27 millimetres squared.

And the base is 76, subtract 12, subtract 12, which is equal to 52.

So the area of the parallelogram is 27 multiplied by 52, which is equal to 1,404 millimetres squared.

And then any to add on the area of the triangles, which gives me 1,819 millimetres squared as the total area.

The final question, a jewellery designer has made a pendant using a triangle with` a smaller triangle, a hole in the middle.

So the hole has an area, a quarter of the whole pendant, and we need to find the area of the red potent of the pendant.

So the area of the pendant is 3.

8 multiplied by its perpendicular height, four centimetres divided by two, which gives us 7.

6 centimetre squared.

The area of the hole was a quarter of that.

So 7.

6 divided by four, which is equal to 1.

9 centimetre squared to so find that area of the red part.

We need to do the area of the whole pendant 7.

6, subtract the area of the whole 1.

9, which means that the area is 55.

7 centimetres squared.

Now it's time for your final quiz, pause the video and complete the quiz and click restart.

Once you finished great, what today you fix in our next lesson, we'll be solving problems involving the calculation and conversion of units of area.

I'll see that.