This powerpoint document discusses measuring shapes and space by explaining perimeter, area, and volume. It provides formulas and examples for calculating the perimeter and area of various shapes including rectangles, triangles, trapezoids, circles, and composite shapes made up of multiple basic shapes. Key formulas presented include the circumference of a circle being equal to 2πr or the diameter, and the area of a circle being equal to πr2. An example composite shape is used to demonstrate calculating total area by finding the individual areas of each component shape.

1. Ra
Measuring Shape and Space
This powerpoint is intended to
be read in stages at the
reader’s own pace.
The main emphasis is to help
adults understand
Perimeter, Area & Volume

2. Units of Measurement
When we measure distances we use whole
metres or parts of metres (centimetres
or millimetres)
Some people might use yards or parts of yards (feet and inches)
We will concentrate on Metric units

3. Perimeter
The distance around a shape!
Shape 1
Shape 2
6cm
5cm
10cm
5cm
8cm

4. Working out
Shape 1 is a rectangle, what is its
perimeter?
Shape 2 is a Trapezium, what is its
perimeter?

5. Perimeter
Not all sides are labelled – These
need to be worked out!
20 cm
32 cm
15cm
6 cm
5cm
5cm

6. Working out
What is the Perimeter of the shape on
the previous Slide?

7. Area
Squared Units We measure flat surfaces
In square units so we must know how wide
A shape is and how high
= one square unitIf
Then this square has fifteen rows and
Fifteen columns of unit squares
So the area of the large square
Is 15 x 15 = 225 units 2

8. Area

9. Working out
2
2
2
2
= 1 x 1 = 1 unit
= 2 x 2 = 4 unit
= 3 x 3 = 9 unit
= 4 x 4 = 16unit
2
2
2
2

10. Volume
Cubed units

11. Working out
On the previous slide we could fit three
and a half unit cubes horizontally, we
could fit three and a half vertically and
we could fit three and a half from front
to back. So we have measured in three
directions (Dimensions). If we now
multiply these dimensions together we
get 3.5x3.5x3.5= 42.875 units3

12. Circles
What do we call the distance from the centre to the
outside of a circle?
RADIUS

13. Circles
The Distance all the way across a circle is the
DIAMETER
The diameter is double the radius

14. Circumference
• The Circumference is the distance all
the way round the outside of a circle.
• This is another name for the Perimeter
of a Circle

15. Circumference
• The Circumference is the distance all
the way round the outside of a circle.
• A larger Circle will have a larger
Circumference (So the bigger the
Radius; the bigger the Circumference!)

16. Calculating the Circumference
Let’s consider the circle below, and say that it has a
Radius that measures 10metres
RADIUS Do you Know a Formula
that we can use to calculate
The Circumference?

17. Formulas for Circumference
• Circumference= 2 x x Radius
• Or C= 2 r
• Or C= d
• (Because 2r= diameter=d)
• is a special number for Circles= 3.14

18. Working out

19. Calculating the Circumference
Let’s consider the circle below, and say that it has a
Radius that measures 10metres
Do you Know a Formula
that we can use to calculate
The Circumference?
C= 2 r
So we can now calculate the Circumference
C= 2 x 3.14 x 10 = 62.8m

20. Calculating the Area of a Circle
Let’s consider the circle below, and say that it has a
Radius that measures 10metres
RADIUS
The Area here is the flat
surface coloured blue.
Do you know a formula
that we can use to
calculate
The Area?

21. Formula for the Area of a Circle
• Area = x Radius squared
• Or A= r
Remember to do r x r first then x
is a special number for Circles= 3.14
2

22. Working out

23. Calculating the Area of a Circle
Let’s consider the circle below, and say that it has a
Radius that measures 10metres
rA=
2
So Here Area= 3.14 x (10 x 10)
A= 314m
2

24. Area of a circle
• Now you practice with these circles
1
2
3
Area when diameter is 30 cm
Circumference of a circle radius = 35 metres
Area when diameter is 20 inches
You can use a calculator if you like! Or say = 3

25. Composite shapes
• A composite shape is one that is
constructed from two or more
different shapes
• These different shapes could be a
combination of Rectangles, Circles,
Squares, or Triangles.
• All flat shapes will have a perimeter and
some area

26. Example of A Composite Shape
What in formation do you need?

27. Working out

28. Example of A Composite Shape
We now know the area of the
rectangle= 16x3 cm= 48 cm
3cm 16 cm
2

29. Example of A Composite Shape
We can now see the two
triangles are the same size so
their combined area is the same
as a rectangle 3cm x4cm= 12cm
4 cm
4 cm
2
3cm

30. Example of A Composite Shape
Let’s calculate the area of the
large half Circle then take away
the area of the small half circle
So far our Area running total is 48+ 12 cm2
3 cm8 cm

31. Working out

32. Example of A Composite Shape
Area of Large = 0.5 x x (8x8) = 0.5x3.14 x 64 = 100.48cm
3 cm8 cm
2
Area of small = 0.5 x x (3x3) = 0.5x3.14 x 9 = 14.13cm
2
Area shaded Blue= 100.48-14.13= 86.35 cm

33. Example of A Composite Shape
So we now have a total Area = 48+12+86.35= 146.35 cm
2

34. Formulas for Area
Area of Rectangle or Square
= Length X Width
Area of a Triangle = ½ X Base X Height