- 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 cm3 = 1 Ml (millilitre)
- 1000 cm3 = 1 L (litre)
- 100 cm3 = 1 dl (decilitre)
- 1 m3 = 1000 litre
- 1000000 cm3 = 1 m3
- 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 = S2
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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