Scale factors, scale diagrams and maps

A road has a length of 1.6 kilometres. The road is shown on a map with a scale of 1: 20 000 Work out the length, in centimetres, of this road on the map.

The accurately drawn diagram shows two points, C and D, on a map.

Find the bearing of D from C.

The scale of the map is 1 cm represents 4 km.

Work out the real distance from C to D.

A map has a scale of 1: 25 000 On the map, a road has a length of 14 cm. Work out the real length of the road. Give your answer in kilometres.

A playground is in the shape of a right-angled triangle.

Dan makes a scale drawing of the playground. He uses a scale of 1 cm represents 5 m The area of the playground on the scale drawing is 28 cm² The real length of QR is 40 m Work out the real length of PQ.

A map has a scale of 1 cm represents 4 km. On the map, the distance from town A to town B is 8 cm.

Work out the real distance, in km, from town A to town B.

The real length of a road is 10 km.

Work out the length of the road on the map. Give the units of your answer.

Matt is drawing a scale diagram. 1 cm represents 5 m. He draws a line 3 cm long.

What real distance does the line represent?

The real distance between two points is 20 m.

What is the distance between the two points on the scale diagram?

The floor plan of a house is drawn using a scale of 1: 50 On the plan, a room in the house has a floor area of 48 cm² Work out the real area of the floor of this room. Give your answer in m²

The diagram shows three motorway service stations P, Q and R on a map.

The map has a scale of 1 cm = 4 km. Work out the real distance from P to R.

14Jenny drives from London to Swindon at an average speed of 54 miles per hour. She drives for 1 hours.

Work out the distance from London to Swindon.

Aleksy is using a map. The map has a scale of 1: 25 000 On the map a road has a length of 6 cm.

Work out the length, in kilometres, of the real road.

On a scale drawing, a building has length 12.4 cm and width 9.4 cm. The real length of the building is 62 metres. Work out, in metres, the real width of the building.

The accurately drawn map shows the positions of three points, A, B and C, in a field.

Scale: 1 cm represents 150 metres Parveen walks in a straight line from A to B. She then walks in a straight line from B to C. Susan walks in a straight line from A to C. Parveen walks more metres than Susan.

How many more?

Find by measurement the bearing of A from C.

The diagram shows a rectangle.

On the centimetre grid below, draw an accurate scale drawing of this rectangle. Use a scale of 1 cm to represent 5 m.

The diagram shows two places on a map.

Scale: 1 centimetre represents 20 kilometres

What is the actual distance, in kilometres, from Shelton to Trilby?

On a scale drawing, the scale is given as 1: 1200

How many metres does 5 centimetres represent on this drawing?

The diagram shows two points, A and B, on a map.

Scale: 1 to 25 000

Find the bearing of B from A.

Work out the real distance between A and B. Give your answer in kilometres.

Here is a plan of a kitchen drawn to a scale of 1: 30

A B

Sam is going to put a small table in the kitchen. The table has to be more than 180 cm from A more than 150 cm from BC Show, by shading on the diagram, the region where Sam can put the table.

The accurate scale diagram shows a telephone mast and a box.

The box has a real width of 1.5 metres.

Find an estimate for the real height, in metres, of the telephone mast.

A map has a scale of 1 cm to 14 km.

On the map, the distance between Manchester and London is 18.8 cm.

What is the real distance, in km, between Manchester and London?

The diagram shows a scale drawing of a tennis court.

The scale of the drawing is 1: 200

Work out the perimeter of the real tennis court. Give your answer in metres.

Here is a map of an island.

A straight road joins the two villages, Backley and Cremford.

Work out the real distance between the two villages.

Find the bearing of Cremford from Backley.

The picture shows a bus next to a building. The bus has a length of 12 m.

The bus and the building are drawn to the same scale.

Work out an estimate for the height, in metres, of the building.

The diagram shows a tree and a man.

The man is of average height. The tree and the man are drawn to the same scale.

Write down an estimate for the real height, in metres, of the man.

Find an estimate for the real height, in metres, of the tree.