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

110 yards75 yard s

and 75 yards wide

110 yards75

yard s

110 yards75

yard s110 yards

75 y

ard

s

What is the perimeter of the football pitch?

110 yards

75 yard

s110 yards

75

ya

rds

110 + 75 + 110 + 75 = 370 yards

Our classroom is approximately

8 metres by 5 metres

What is the perimeter?

8 m5

m Our classroom

8 m5

m Our classroom

8 m5 m

8 + 5 + 8 + 5 = 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?

3 + 4 + 5 = 12 metres

13 cm

12 cm

5 c

m

The perimeter of this triangle?

5 + 12 + 13 = 30 cm

These TETROMINOES are all made from four squares

Do they all have the same perimeter?

I get the following:

10 units

10 units10 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

20 yards

60 yards

If you have a calculator, then you could say it is 3.1, or 3.14, or 3.142 times the diameter.

If you have a posh calculator, you could use the π button.

10 yards

20 yards

π• 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…

3.14159265358979323846264338327950288419716939937510582097494459230781640628620899862803482534211706798214808651328230664709384460955058223172535940812848111745028410270193852110555964462294895493038196442881097566593344612847564823378678316527120190914564856692346034861045432664821339360726024914127372458700660631558817488152092096282925409171536436789259036001133053054882046652138414695194151160943305727036575959195309218611738193261179310511854807446237996274956735188575272489122793818301194912983367336244065664308602139494639522473719070217986094370277053921717629317675238467481846766940513200056812714526356082778577134275778960917363717872146844090122495343014654958537105079227968925892354201995611212902196086403441815981362977477130996051870721134999999837297804995105973173281609631859502445945534690830264252230825334468503526193118817101000313783875288658753320838142061717766914730359825349042875546873115956286388235378759375195778185778053217122680661300192787661119590921642019…

Pause for Play

8 cm

8 cm

6 cm

4 cm

Which has the greatest

perimeter?

Area

Return to the classroom

8 m5

m What do we use to measure

area?

Square metres

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

8 m5

m How many square metres?

8 m2

8 m5

m

5 x 8 = 40 square metres, or 40 m2

Pause for Play

Draw some rectangles with an area of 20 square centimetres.

Do they have the same perimeter?

110 yards75

yard s

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

110 yards75

yard s

110 x 75 = 8250 square yards

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

Start with a simple one:

12 cm

5 c

m

What if we ‘double up’?

12 cm

5 c

m

Area of the rectangle?

12 cm

5 c

m

Area of the triangle?

Area of the rectangle = 60 cm2

12 cm

5 c

m

Area of the triangle = 30 cm2

Slightly more complicated:

3 cm

8 cm

But we can still ‘double up’

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 cm2

And a parallelogram?

Make some cuts:

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 cm2

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 m 4 m 3 m

9 m

What is the area of this trapezium?

5 m

2 m 4 m 3 m

9 m

One possible method, giving 32.5m2:

5 m2 20 m2 7.5 m2

5 m

4 m

9 m

Another method

25.3252

)94(m=×+

c

a

b

And the formula:

cba ×+=

2

)( trapezium a of Area

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

πr

And the area will be π r × r

r

πr

So area of a circle = π × r × r = π × r2

And a final return to our little football circle:

Area = π × r2 = 3.14 × 102 = 3.14 × 100 = 314 square yards

10 yards

Got it?

For Circles:

Cherry Pie’s DeliciousApple Pies R 2

In other words

C = π dA = π r2

Pause for Play

8 cm

8 cm

6 cm

4 cm

Which has the greatest area?

Hint: S

quare 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