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Britain is officially metric in line with the rest of Europe
Britain is officially metric in line with the rest of Europe
However, imperial measures are still in use, especially for road distances, which are measured in miles. Imperial pints and gallons are 20 per cent larger than US measures.
Imperial to Metric
Imperial to Metric
1 inch = 2.5 centimetres
1 foot = 30 centimetres
1 mile = 1.6 kilometres
1 ounce = 28 grams
1 pound = 454 grams
1 pint = 0.6 litres
1 gallon = 4.6 litres
Metric to Imperial
Metric to Imperial
1 millimetre = 0.04 inch
1 centimetre = 0.4 inch
1 metre = 3 feet 3 inches
1 kilometre = 0.6 mile
1 gram = 0.04 ounce
1 kilogram = 2.2 pounds
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How do we measure area?
How do we measure area?
Area is a measure of how much space there is inside a shape. Calculating the area of a shape or surface can be useful in everyday life – for example you may need to know how much paint to buy to cover a wall or how much grass seed you need to sow a lawn.
This section covers the essentials you need to know in order to understand and calculate the areas of common shapes including squares and rectangles, triangles and circles.
Calculating Area Using the Grid Method
Calculating Area Using the Grid Method
When a shape is drawn on a scaled grid you can find the area by counting the number of grid squares inside the shape.
In this example there are 10 grid squares inside the rectangle.
In order to find an area value using the grid method, we need to know the size that a grid square represents.
This example uses centimetres, but the same method applies for any unit of length or distance. You could, for example be using inches, metres, miles, feet etc.
In this example each grid square has a width of 1cm and a height of 1cm. In other words each grid square is one 'square centimetre'.
Count the grid squares inside the large square to find its area..
There are 16 small squares so the area of the large square is 16 square centimetres.
In mathematics we abbreviate 'square centimetres' to cm2. The 2 means ‘squared’.
Each grid square is 1cm2.
The area of the large square is 16cm2.
Although using a grid and counting squares within a shape is a very simple way of learning the concepts of area it is less useful for finding exact areas with more complex shapes, when there may be many fractions of grid squares to add together.
Area can be calculated using simple formulae, depending on the type of shape you are working with.
The remainder of this page explains and gives examples of how to calculate the area of a shape without using the grid system.
The simplest (and most commonly used) area calculations are for squares and rectangles.
The simplest (and most commonly used) area calculations are for squares and rectangles.
To find the area of a rectangle, multiply its height by its width.
To find the area of a rectangle, multiply its height by its width.
For a square you only need to find the length of one of the sides (as each side is the same length) and then multiply this by itself to find the area. This is the same as saying length2 or length squared.
For a square you only need to find the length of one of the sides (as each side is the same length) and then multiply this by itself to find the area. This is the same as saying length2 or length squared.
Real life is not as simple as squares or rectangles
Real life is not as simple as squares or rectangles
Parallelogram
Parallelogram
When working out the area of a parallelogram it is important to measure the height of the shape and not the length of the sides. From the diagram you can see that the height is the distance between the top and bottom sides of the shape - not the length of the side.
Areas of Triangles
Areas of Triangles
It can be useful to think of a triangle as half of a square or parallelogram.
It can be useful to think of a triangle as half of a square or parallelogram.
Here are some examples to try
Here are some examples to try
Work out area as normal for example 4cm x 4cm = 16cm then divide by 2 = 8cm which is the area of a triangle that has a height of 4cm and a width of 4cm.
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In real-life situations you may be faced with a problem that requires you to find the area of a triangle, such as:
In real-life situations you may be faced with a problem that requires you to find the area of a triangle, such as:
You want to paint the gable end of a barn. You only want to visit the decorating store once to get the right amount of paint. You know that a litre of paint will cover 10m2 of wall. How much paint do you need to cover the gable end?
You need three measurements:
A - The total height to the apex of the roof.
B - The height of the vertical walls.
C - The width of the building.
In this example the measurements are:
A - 12.4m
B - 6.6m
C - 11.6m
The next stage requires some additional calculations. Think about the building as two shapes, a rectangle and a triangle. From the measurements you have you can calculate the additional measurement needed to work out the area of the gable end.
Measurement D = 12.4 – 6.6
D = 5.8m
You can now work out the area of the two parts of the wall:
Area of the rectangular part of the wall: 6.6 × 11.6 = 76.56m2
Now using the information and knowledge & skills you have developed work out the total area of the gable end.
Now using the information and knowledge & skills you have developed work out the total area of the gable end.
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Area of Circles
Area of Circles
In order to calculate the area of a circle you need to know its diameter or radius.
In order to calculate the area of a circle you need to know its diameter or radius.
You need the radius to work out the area of a circle, the formula is:
You need the radius to work out the area of a circle, the formula is:
circle area = πR2.
This means:
π = Pi is a constant that equals 3.142.
R = is the radius of the circle.
R2 (radius squared) means radius × radius.
Therefore a circle with a radius of 5cm has an area of:
3.142 × 5 × 5 = 78.55cm2.
A circle with a diameter of 3m has an area:
First, we work out the radius (3m ÷ 2 = 1.5m)
Then apply the formula:
πR2
3.142 × 1.5 × 1.5 = 7.0695.
The area of a circle with a diameter of 3m is 7.0695m2.
Calculating Volume
Calculating Volume
This section explains how to calculate the volume of solid objects, i.e. how much you could fit into an object if, for example, you filled it with a liquid.
WARNING!
Volume can also be expressed as liquid capacity.
Metric System
In the metric system liquid capacity is measured in litres, which is directly comparable with the cubic measurement, since 1ml = 1cm3. 1 litre = 1,000 ml = 1,000cm3.
Imperial/English System
In the imperial/English system the equivalent measurements are fluid ounces, pints, quarts and gallons, which are not easily translated into cubic feet. It is therefore best to stick to either liquid or solid volume units.
How you refer to the different dimensions does not change the calculation: you may, for example, use 'depth' instead of 'height'. The important thing is that the three dimensions are multiplied together. You can multiply in which ever order you like as it won't change the answer.
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Example 1
Calculate the volume of a cylinder with a length of 20cm, and whose circular end has a radius of 2.5cm.
First, work out the area of one of the circular ends of the cylinder.
The area of a circle is πr2 (π × radius × radius). π (pi) is approximately 3.14.
The area of an end is therefore:
3.14 x 2.5 x 2.5 = 19.63cm2
The volume is the area of an end multiplied by the length, and is therefore:
19.63cm2 x 20cm = 392.70cm3
Example 2
Which is bigger by volume, a sphere with radius 2cm or a pyramid with base 2.5cm square and height of 10cm?
First, work out the volume of the sphere.
The volume of a sphere is 4/3 × π × radius3.
The volume of the sphere is therefore:
4 ÷ 3 x 3.14 × 2 × 2 × 2 = 33.51cm3
Then work out the volume of the pyramid.
The volume of a pyramid is 1/3 × area of base × height.
Area of base = length × breadth = 2.5cm × 2.5cm = 6.25cm2
Volume is therefore 1/3 x 6.25 × 10 = 20.83cm3
The sphere is therefore larger by volume than the pyramid
Worked example
Calculate the volume of a water cylinder with total height 1m, diameter of 40cm, and whose top section is semi-spherical.
You first divide the shape into two sections, a cylinder and a semi-sphere (half a sphere).
The volume of a sphere is 4/3 × π × radius3. In this example the radius is 20cm (half the diameter). Because the top is semi-spherical, its volume will be half that of a full sphere. The volume of this section of the shape therefore:
0.5 × 4/3 × π × 203 = 16,755.16cm3
The volume of a cylinder is area of the base × height. Here, the height of the cylinder is the total height less the radius of the sphere, which is 1m – 20cm = 80cm. The area of the base is πr2.
The volume of the cylindrical section of this shape is therefore:
80 × π × 20 × 20 = 100,530.96cm3
The total volume of this water container is therefore:
100,530.96 + 16,755.16 = 117,286.12cm3.
Remember 1000cm cubed in a litre
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Let's look at some design using some measurement techniques
Let's look at some design using some measurement techniques
The customer wants as much kitchen storage with a base unit as possible
The customer wants as much kitchen storage with a base unit as possible
Using this LINK search through the available units and outline in the quiz below how many units would fit into the kitchen drawing featured on the left.
The dimensions of the kitchen sink are 900mm long and the hob/cooker is 750mm long. Take these into consideration when looking at the base units. Also the customer has specified that they want a corner unit between the sink and the cooker/hob.
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Tiling the floor using your area calculations
Tiling the floor using your area calculations
Look at the drawing, work out the area of the room. Before installing the kitchen the floor needs to be tiled. It is to be tiled with the following tiles;
GREY POLISHED TILE How many will you need to tile the floor, add onto your total an extra 10% for cuts and breakages?
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