Lesson video

Hello, my name's Ms. Parnham.

In this lesson, we're going to learn how to find the area of a semicircle and a quarter circle.

Before we work out the area of a semicircle or quarter circle, let's refresh our memory on the area of a circle.

Here we have a circle with diameter, 12 centimetres.

And the area of a circle formula is pi r squared.

Now r means radius, and we have a diameter.

So to the diagram, we add a radius of six because we half the diameter to get the radius.

So we're going to square that six and multiply by pi, oh, if you want 36 pi and on our calculators, we find that this is 113 centimetre squared to three significant figures.

Right? Let's look at a semicircle with exactly the same diameter as our circle.

So the formula, this time is pi r squared divided by two.

So our radius is still six centimetres and it's half 36 pi.

Now it is 18 pi.

And if we leave the.

If we've left 113 centimetres accurately on our calculator, we can just half that by dividing it by two.

Let's think about a quarter circle with exactly the same radius.

Notice we don't draw a diameter on a quarter circle.

So the quality circle is pi r squared divided by four.

So the 36 pi divided by four to find nine pi.

And if we want to take our accurate answer of 113 centimetre square and divide it by four, we should have 28.

3 centimetre squared to three significant figures.

Here's some questions for you to try.

Pose the video, to complete the task and restart the video when you're finished.

Here are the answers.

In question two parts C, did you notice it was labelled with a diameter, not a radius if you needed to have this before using it in the formula to work out the area.

So you could have written 40 under half pi, metre squared as well, or alternatively 81 pi over two, metre squared would also be a correct answer.

Here are some more questions for you to try.

Pause the video to complete the task and restart the video when you're finished Here are the answers.

Always made sure you have the correct units of measurement because you start with a measurement as a distance, a radius or a diameter is a distance, but your answer is always a measurement of area.

So it needs to be centimetre squared, metre squared or millimetre squared.

As mentioned previously, did you notice part d you had a diameter, so you did need to know to divide that by two, to get the radius first.

Now here, we have a shape made of quarter circle, a rectangle and a triangle.

So what we're going to do is work out the area of each shape individually.

And then at the end, combine them to get the area of the compound shape.

Let's start with a rectangle.

This has dimensions of 12 and seven.

So multiplying those together gives us 84 centimetre squared.

Now the triangle, we need to work out some of the dimensions on here.

So we have a total length on the bottom of 20 and the length of the rectangle is 12.

So the triangle is going to have a base of eight.

And the height of the triangle is made by adding the seven centimetres, which is the width of the rectangle to 12, because the radius of the quarter circle is 12.

So that gives us the 19.

Now to work out the area of a triangle we multiply the height on the base together and divide by two.

So that's where 76 centimetre squared comes from.

And finally, let's do the area of the quarter circle.

We have a radius of 12.

So this is pi r squared divided by four.

So the 144 pi divided by four gives us 36 pi, which is 113 centimetre square to three significant figures.

But don't forget.

We need to add all three ounces together to get the total area of the shape.

So to three significant figures.

That's 273 centimetres squared.

Let's have a look at another shape.

This time we have a smallest semicircle chopped out of a larger semicircle.

And we have the diameter of the smallest semicircle and then the extra distance to take us to the largest semicircle.

So let us work out the semicircles individually, and then do a subtraction in order to find that shaded area.

So if we have a diameter of eight metres, we must have a radius of four metres.

So pi r squared divided by two gives us eight pi for the smallest semicircle.

The larger semicircle has a radius of eight metres because it is four metres from the smaller semicircle with another four metres added on.

So this gives us pi multiplied by eight squared divided by two or 64 pi divided by two or 32 pi.

So actually we can do the subtraction using the answers that are written in terms of pi.

So 32 pi subtract eight pi gives us 24 pi and then placing that into our calculator and we get the answer of 75.

4 metre squared to three significant figures.

There's some questions for you to try.

Pause the video to complete the task and restart the video when you're finished.

Here are the answers.

Part C needs to do to calculate the radius of the quater circle by subtracting 2.

5 from the whole length of the rectangle, which is 4.

5.

So you should have got 1.

9 and calculated with that.

Here some further questions for you to try.

Pause the video to complete the task and restart the video when you're finished.

Here are the answers.

Maybe noticed in part B you could form a circle from the two semicircles.

So 68 squared subtract pi multiplied by 34 squared would get you straight to the solution for that question.