Perimeter

The perimeter of a shape is the distance around it.

The perimeter of this rectangle is 20 cm. If we start from A and move around it in a clockwise direction, we travel a distance of .

Area's of shapes

Counting squares to find the area of a shape

The squares on this grid are , so the area of each square is .

What is the area of the shape on this grid? The shape covers 8 squares, so the area is .

Being well-organised helps. One idea is to count down the rows and tick them off as you do so. This will help to avoid mistakes.

 

 

Area of triangles

You can find the area of triangles by following these steps:

• make the triangle into a rectangle
• count the squares in the rectangle
• halve the number of squares in the rectangle (divide them by 2)

To find the area of this triangle,

you first make it into a rectangle:

 

The area of the rectangle is 30 cm ² so the area of the triangle will be half of this. The area of the triangle is .

Circles (pi)

Circle terminology

Here is a list of words associated with circles. Are they familiar to you?

Put your mouse on each word to highlight an example.

These are the abbreviations that we will use:

• C = circumference
• A = area
• d = diameter
• r = radius

Circumference of a circle

The circumference is the length of the edge around a circle.

For any circle, the circumference is:

Or in symbols:

This is true for all circles and so ... is therefore a special, unique number, and we represent it with the Greek letter .

 (The symbol is called 'pi' in English and is pronounced 'pie').

So we can write the formula for the circumference of a circle as:

However, the diameter is equal to , (), so we can also write this formula as:

It does not matter which of these formulae you use. But you must be careful to use the correct length for the formula (the radius or diameter).

 

Pythagoras Theorem

Finding the remaining side of a right-angled triangle

Look at the diagrams below. The areas of the squares are marked inside them (the diagrams are drawn to different scales). How are the squares' areas related to each other?

Did you spot it?

If you add the areas of the smallest two squares you get the area of the largest square.

In any right-angled triangle, the square of the longest side is the sum of the squares of the other two sides. This can be written in the formula:

Where is the longest side.

That is Pythagoras' theorem.

Using Pythagoras theorem to solve problems

You can work out other mathematical problems using Pythagoras' theorem. For instance, if you know two sides of a right-angled triangle, you can find the third like this:

1. square (multiply by itself) the lengths you know
2. add or subtract them
3. find the square root

For these questions you will need to use the button on your calculator.

Bar Graphs 23/10/2015

Types of bar chart

Bar charts or bar graphs represent data as vertical blocks or columns.
The X axis shows what type of data each column represents, and the Y axis shows a value for that type of data. For example, in a rainfall graph, each column on the X axis represents a month of the year, with the height of each column on the Y axis showing the amount of rainfall in that month.

Compound

It is possible to split each column into sections to show the breakdown of data. For example, the employment data shown on the previous page could have been represented as three columns on a bar chart. The three columns would represent the three countries, with each column subdivided into sections showing primary, secondary and tertiary in different colours. This type of bar chart is sometimes called a compound bar chart.

Comparative

It is also possible to compare two sets of data on a bar chart - for example, measuring rainfall in two countries over the same period. This type of bar graph is called a comparative bar graph.
The chart below compares the tourism data for the UK in October 2001 with October the previous year. The graph shows how tourism declined after the terrorist attack in America in September 2001.

Bar chart showing decline in tourism to the UK

3D Shapes

3D solid shapes

Here are some common solid shapes.

Prisms and pyramids

A prism is a 3D shape which has a constant cross section - both ends of the solid are the same shape and anywhere you cut parallel to these ends will give you the same shape.

For example, in the prism below, the cross section is a hexagon.

This is called a hexagonal prism.

A pyramid has sloping faces that meet at a vertex.

Square-based pyramid

Tetrahedron

Drawing 3D shapes on isometric paper

You can use isometric paper to draw 3D shapes.

Remember to hold the isometric paper so that you can see vertical rows of dots!

This cube has been drawn using the dots as guides. The vertical lines are always vertical, but the horizontal lines are drawn at an angle, when drawn on isometric dotted paper. You could get some isometric paper and draw the cube yourself.

Perimeter 9th October Compund shapes

Compound shapes

Sometimes the shape is more complicated. In this case you need to calculate 'missing' lengths and be particularly careful to include all the sides.

Perimeter = 2 + 2 + 3 + 3 + 5 + 5 = 20 cm

Question

A plan of a play area is shown below: