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Shape, Space and Measure (Intermediate) - Length and Area
 
Units of Length | Area
Units of Length

On the metric system, we use the following units for length. Millimetres(mm), Centimetres(cm), Metres(m) and Kilometres(km).

 10 mm= 1cm 
100cm= 1m 
1000m=1km
Perimeter
This is the distance around the outside of a shape. To calculate the perimeter we add together the lengths of the sides of the shape.
For Example:
1) Calculate the perimeter of the rectangle ABCD
length and area1
Perimeter=15+15+8+8 = 46cm
 
Note: If we use L for length and W for width, the perimeter(P) can be written as a formula:
 
P=2L+2W
2) Calculate the perimeter(P) of the shape below.
length and area2
P=5+5+3+3+2+2+10+4 = 34cm
Note: In this example we need to work out the length of 4cm. (10-6=4). The other missing lengths 2cm and 5cm can be found from the shape.
 

Area

Area is the space inside a shape. It is measured by dividing the shape into squares and counting them. If the squares are of side 1cm, then we can use the units cm2.
Irregular shapes can be drawn on a grid and the area estimated by counting the squares. Parts of a square need to be added to make a whole square.
For example:
Estimate the area of the shape below:
length and area3

Area = 3½ squares 
Regular shapes for example Triangles, Rectangles and Kites, have a formula for calculating the area.
 
Area of a Rectangle
Area=Length x Width
 
For example: 
Calculate the volume of the cuboid shown below.Calculate the area of the rectangle ABCD.
length and area4
Area=15 x 8= 120cm2 (Note the units of area: cm2 )
 
Area of a Triangle
Area = ½ x Base x Height
 
For example:
Calculate the area of triangle ABC.
length and area5
Area=1/2 x 10 x 6= ½ x 60 = 30cm2
 
(Note: 10 x 60 would give the area of the rectangle standing on BC, the area of the triangle is half this area).
 
Area of a Parallelogram
Area = Base x Height
 
For Example:
Calculate the area of the parallelogram PQRS.
length and area6
Area = 10 x 6 = 60cm2
Area of a Kite and Rhombus
Area = ½ (the product of the diagonals)
For Example
Calculate the areas of the kite ABCD and the rhombus LMNO.
length and area7
Area of ABCD and LMNO = ½ x 10 x 6 =30cm2
Area of a Trapezium
Area = ½(the sum of the parallel sides) x the height
For Example
Calculate the area of the trapezium ABCD.
length and area8
Area = ½ (10+20) x 5 = ½ x 30 x 5 = 75cm2
Note Sometimes the area is given in a problem and we are asked to calculate the length of one of the sides.
For example
Calculate the length of QR in the triangle, given that the area is 20cm2
length and area9
20 = ½ x 4 x QR
20 = 2 x QR
QR = 10cm
Compound shapes
In some problems it is necessary to divide the shape into regular shapes. We can add or subtract areas.
For example
Calculate a)the total area and b) the shaded area in the diagram below.
length and area10
a) Total Area = Area A + Area B
=(2x3) + (5x10)
= 6+50
= 56cm2 		b) Shaded Area = 56 – (2x2)
= 52cm2