Perimeter and Area A look at a few basic shapes

Perimeter

This little square represents a bigger square, one yard in length, and one yard in width.

And this is Stamford Bridge (football!)

Stamford Bridge football pitch is 110 yards long 110 yards

75 yards and 75 yards wide

110 yards 75 yards

110 yards 75 yards 110 yards 75 yards What is the perimeter of the football pitch?

110 yards 75 yards 110 yards 75 yards = 370 yards

Our classroom is approximately 8 metres by 5 metres What is the perimeter?

8 m 5 m Our classroom

8 m 5 m Our classroom 8 m 5 m = 26 metres

Question? How do we find the perimeter of a triangle? Answer: Let Google Maps do the measuring for us.

The perimeter of the Bermuda Triangle is approximately 4700 km

Or 2922 miles

5 m 4 m 3 m The perimeter of this triangle? = 12 metres

13 cm 12 cm 5 cm The perimeter of this triangle? = 30 cm

These TETROMINOES are all made from four squares Do they all have the same perimeter?

I get the following: 10 units 8 units 10 units

Pause for Play Draw some shapes with a perimeter of 20 centimetres.

Let’s go back to Stamford Bridge What is the perimeter of that circle in the middle? Actually, on a circle it is called the circumference

According to BBC Sport, it has a radius of 10 yards. Which is from the centre of the circle to the circumference. 10 yards

If the radius is 10 yards, then the diameter is 20 yards. The circumference is about three times the diameter. So the circumference is about 3 x 20 = 60 yards 10 yards 20 yards

60 yards

If you have a calculator, then you could say it is 3.1, or 3.14, or times the diameter. If you have a posh calculator, you could use the π button. 10 yards 20 yards

Pi – the Greek letter π, which represents the ratio of the circumference to the diameter of a circle. We can’t actually write it down exactly. But we can write it to as many decimal places as we want.

If you have a computer you could use a thousand decimal places…

…

Pause for Play 8 cm 6 cm 4 cm Which has the greatest perimeter?

Area Return to the classroom

8 m 5 m What do we use to measure area?

Square metres (or square yards, or square inches, or square centimetres…)

8 m 5 m How many square metres?

8 m 2

8 m 5 m 5 x 8 = 40 square metres, or 40 m 2

Pause for Play Draw some rectangles with an area of 20 square centimetres. Do they have the same perimeter?

110 yards 75 yards What, in square yards, is the area of Stamford Bridge?

110 yards 75 yards 110 x 75 = 8250 square yards

What about a triangle - how do we find the area?

Start with a simple one: 12 cm 5 cm

What if we ‘double up’? 12 cm 5 cm

Area of the rectangle? 12 cm 5 cm Area of the triangle?

Area of the rectangle = 60 cm 2 12 cm 5 cm Area of the triangle = 30 cm 2

Slightly more complicated: 3 cm 8 cm

But we can still ‘double up’

8 cm 3 cm

Area of rectangle = 3 x 8 = 24 8 cm 3 cm Area of triangle = (3 x 8) ÷ 2 = 12 cm 2

And a parallelogram?

Make some cuts:

And then some swaps:

And we are back to a rectangle:

The original: 3 cm 7 cm

And the new one: 7 cm 3 cm

The area = 7 x 3 = 21 cm 2 7 cm 3 cm

Pause for Play Experiment with square paper and see if you can find a method of calculating the area of a trapezium.

5 m 2 m4 m3 m 9 m What is the area of this trapezium?

5 m 2 m4 m3 m 9 m One possible method, giving 32.5m 2 : 5 m 2 20 m m 2

5 m 4 m 9 m Another method

c a b And the formula:

And finally a circle A bit trickier to explain

Chop it up a bit

And rearrange the parts Not a lot of use!

Chop it into smaller sectors

And rearrange the parts again And it is starting to look like something else

Even smaller sectors:

And rearrange the parts yet again And it’s near enough to a rectangle for me!

=

What is the length and width?

The width is the radius of the original circle r

And the length is half the circumference Since the circumference = πd Then half the circumference = πr Because r = ½d

So we have approximately a rectangle r πrπr

And the area will be π r × r r πrπr So area of a circle = π × r × r = π × r 2

And a final return to our little football circle: Area = π × r 2 = 3.14 × 10 2 = 3.14 × 100 = 314 square yards 10 yards

Got it? For Circles: Cherry Pie’s Delicious Apple Pies R 2 In other words C = π d A = π r 2

Pause for Play 8 cm 6 cm 4 cm Which has the greatest area? Hint: Square paper, isometric paper, and a pair of scissors?

And that’s more than enough! Perimeter of shapes made from straight lines Circumference of circles Area of rectangles, triangles, parallelograms and trapeziums Area of circles