- Length
- Mass
- Volume And Capacity
- Time
- Area
- Surface Area
- Volume of Cylinder and Rectangular Shapes
- Perimeter
- Expressing areas of Large Shapes

## Length

The units of length that are used include the following:

- millimetre (mm)
- centimetre (cm)
- decimetre (dm)
- Metre (m)
- Dekametre (Dm)
- Hectometre (Hm)
- Kilometre (Km)

From the illustration:

- 10mm = 1cm
- 10cm = 1dm
- 10dm = 1m
- 10m = 1 Dm
- 10Dm = 1Hm
- 10 Hm = 1Km

The relationship between the units of lengths may be clearly seen if the units are written with a 10 between them.

So to find how many small units are equivalent to another, multiply the number of tens between the units, hence:

- Km 1
- Hm 10
- Dm 100
- M 1000
- dm 10000
- mm 1000000

## Mass

- 1000 g = 1Kg
- 1000 Kg = 1Tonne
- 1000000 g = 1Tonne

## Volume and Capacity

- 1 cm
^{3}= 1 Ml (millilitre) - 1000 cm
^{3}= 1 L (litre) - 100 cm
^{3}= 1 dl (decilitre) - 1 m
^{3}= 1000 litre - 1000000 cm
^{3}= 1 m^{3} - 10 dl = 1 Litre
- 1000ml = 1 Litre

## Time

- 60 Seconds = 1 Minute
- 60 Minutes = 1Hour
- 3600 Seconds = 1 Hour
- 24 Hours = 1 day
- 7 Days = 1 Week

## Area

### Rectangle

Area = Length x Width

A = L X W

### Square

Area = Side x Side

A = S x S

A = S^{2}

### Parallelogram

A = base x Height

A = b x h

### Rhombus

Area = base x height

A = b x h

### Triangle

Area = base x height

A = b x h

### Trapezium

Area = x sum of parallel lines x height

A = (a + b) x h

A = h (a + b)

### Circle, half circle, quarter circle

#### Circle

Area = П x radius x radius

A = П x r x r

A = Пr2

#### Half circle

Area = Area of a full circle ÷ 2

A = П r2

2

A =½ Пr2

#### Quarter circle

A = Area of the full circle ÷ 4

A = Пr2 ÷ 4

A = ¼Пr2

Note: П = 22/7 or 3.14 or 3 1/7

## Surface Area

### Surface Area of a Cylinder

T.S.A = Area of circular ends + area of the curved surface

=2Пr2 + Пdh ( if closed both ends)

T.S.A = Пr2 + Пdh (if open one end )

T.S.A = Пdh (if open both ends/pipe)

### Surface Area of a Cube

T.S.A = Total area of all the six faces

= 6 x L x L

= 6L2 (if closed)

or

= 5L2 (if open one end)

### Surface Area of a Cuboid

T.S.A = Total area for the six faces

= 2 (L x w) + 2 (L x h) + 2 (w x h)

or

= (L x w) + 2 (L x h) + 2(w x h) ( if open on top)

### Surface Area of a Triangular prism

T.S.A = Area of all the 5 faces of the prism

## Volume of Cylinder and Rectangular Shapes

### Volume of a Cylinder

Volume = Base area x height

= Пr2 x height

= Пr2h

### Volume of a Rectangular shape

Volume = Base area x height

V = L x w x h

Note: Depending on the cross-section, the volume of any shape / solid is given by.

V = Area of cross-section x height/length

## Perimeter

#### Perimeter of a Rectangle

P = Length + Length + Width + Width

= L + L + W + W

= 2L + 2W or 2(L + W)

#### Perimeter of a Square

P = L + L + L + L

= 4L

#### Perimeter of a Circle

C = П x diameter

= Пd or 2Пr

Note: Perimeter of a full circle is called circumference

#### Perimeter of a Half a Circle

Perimeter = circumference + diameter

P = ½Пd + d

Note: For triangles and irregular shapes, JUST ADD THE DISTANCE ALL ROUND.

## Expressing area of large shape

Hectare – A shape that measures 100m by 100m

Therefore 1ha = (100 x 100)m2

1 ha = 10000m2

Are – a piece / shape that measures 10m by 10m

Therefore 1 are = 10 x 10

1 are = 100m2

Hence:

1 ha = 10000m21are = 100m2

1ha = 100ares

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