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