Lesson video

Hi, I'm Mr. Chang, and in this lesson, we're going to learn about the area of a trapezium.

Let's look at an example of how we calculate the area of a trapezium, we use the formula area equals ½ h So in this formula, we need to identify what a, b and h are.

Well, a and b are the two parallel sides.

So in this trapezium, the two parallel sides will be the 5 metres and the 9 metres.

So we can substitute the two parallel sides into the formula that like so, the h is the perpendicular height, so that's the right angled height from the base in this trapezium, that would be the 4 metres so we can substitute that into the formula as well.

Now we're also given the sloped height of 480 centimetres or 4.

8 metres.

We don't actually need that in this calculation for the area, so I'm going to ignore it.

Now order operations tells us we must do any operations inside the brackets first, so the brackets is 5 and 9.

Let's do that 5 and 9 is 14.

Now we're in the position now to work out the area by multiplying the 14 by a ½, so that becomes 7 x 4.

So we'll get the final answer of the area the trapezium 28 metres squared.

Let's look at another example of calculating the area of a trapezium.

We've got trapezium drawn in front of us there.

The formula for the area of a trapezium is ½ h.

So what we need to know is the parallel sides now this trapezium is just been rotated.

So the parallel sides are actually the 12 and 15.

So those sides represent a + b, substitute those values in to the formula the height in this trapezium, remember, we must use the perpendicular height.

Now if I think about this trapezium is rotated back round to either the 15th, or the 12th being the base, the perpendicular height would be the 7 centimetres.

Remember, it's got to be the height at a right angle to the base.

So we substitute the 7 into the formula there.

And we get a calculation as displayed on the screen.

So order operations again, we must work out what the two numbers in the brackets add up to.

So that's 27 , 12 and 15 equals 27.

And the calculation becomes ½ x 27 x 7, so let's do the ½ x 27 first, that will be 13.

5.

Multiply that by 7 we get a final answer.

The area of the trapezium is 94.

5 centimetres squared.

Here are some questions for you to try.

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

Here are the answers for the first question.

The question asks us to calculate the area of the trapezia.

Trapezia is just plural for trapezium.

So in part A, we've got perpendicular height to 5 metres, and the two parallel sides are 8 and 12 metres.

So remember the formula for the area of a trapezium is ½ x h.

So when we substitute those values into the formula, we will get ½ x 5.

And when we work that calculation out, we will get an area of 50 metre squared.

Here's another question for you to try.

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

Here is answer for question 2.

So make sure you don't make this common mistake of using the slope height instead of the Perpendicular height.

So Moe's made a simple mistake there of using the 3 when he should have used the 2 centimetres.

In this example, we're told that the area trapezium is 100 centimetres squared, and we've got to work out one of the missing side lengths as marked x.

Looking at the diagram, the side marked x is one of the parallel sides.

So let's think about what the area of the trapezium formula is.

The area is ½ h.

And what we can do is substitute the values that we do know into the formula and create what we know is an equation so we know the area we know one of the parallel sides the parallel side is marked x and we know the perpendicular height.

So when we substitute all those values into the formula, we get this 100= ½ x x 10.

Now because multiplication it's commutative.

And that means we can multiply in any order and it doesn't change the answer, we can do the ½ times 10 first.

So if we did that ½ x 10 = 5, that's what the equation becomes.

So we rearrange the equation now and remove the multiply by 5 by dividing both sides by 5, the equation becomes 20 = 8 + x, subtract 8 from both sides, we get x = 12.

So we've worked out what the missing side length is.

So this missing side length is 12 centimetres.

Here's some 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 3, you've got to calculate a missing side length when you're given the area.

We've just looked at an example that might help you with that if you struggled.

In Question 4.

I would suggest that you draw the diagram out as described in that question.

And substitute the values in your given into the area formula.

And what will help you then is create an equation that you can rearrange to find the perpendicular height and hopefully you get the correct answer with that one.

Here's another question for you to try.

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

Here's the answer for question 5.

So in this question, we're asked if Harry has enough money to seed his garden that is in the shape of a trapezium.

Now, looking at the garden, the parallel sides are 4 metres and 7 metres.

So that makes the perpendicular height 4.

5 metres.

We're also given the slope height of that trapezium which is 5 metres.

I don't need that so I'm going to ignore it.

So using those measurements to work out the area, you should have got the area equals 24.

75 metre squared.

So because the Grass seed cost 3 pounds 50 per square metre, multiply the area by that cost of per square metre should get a cost of 86 pounds 63 are just under that.

And because he only has 85 pounds to spend, you can say that he does not have enough money.

That's all for this lesson.

Thanks for watching.