Similar Shapes

Instructions Try your best to answer the questions above. Type your answers into the boxes provided leaving no spaces. As you work through the exercise regularly click the "check" button. If you have any wrong answers, do your best to do corrections but if there is anything you don't understand, please ask your teacher for help. When you have got all of the questions correct you may want to print out this page and paste it into your exercise book. If you keep your work in an ePortfolio you could take a screen shot of your answers and paste that into your Maths file.

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Description of Levels

Level 1 - Lengths of similar shapes

Level 2 - Areas of similar shapes

Level 3 - Volumes of similar shapes

Level 4 - Mixed questions

Exam Style Questions - A collection of problems in the style of GCSE or IB/A-level exam paper questions (worked solutions are available for Transum subscribers).

Similar Parts Puzzle - Use the colours to dissect the outlines into similar parts.

More on Enlargements including lesson Starters, visual aids, investigations and self-marking exercises.

Square in Rectangle - An advanced lesson Starter.

Answers to this exercise are available lower down this page when you are logged in to your Transum account. If you don’t yet have a Transum subscription one can be very quickly set up if you are a teacher, tutor or parent.

Curriculum Reference

See the National Curriculum page for links to related online activities and resources.

Help

Enlargements

If you enlarge the dimensions of a polygon by multiplying them by a number (scale factor), the area is increased by the square of that factor.

For example if the sides of a rectangle are enlarged by a factor of 6, the area of the rectangle increases by a factor of 6²

If the length of the original rectangle was 5cm and the width was 2cm then after enlargement they would be 30cm and 12cm respectively.

The area of the original rectangle is 5cm x 2cm = 10cm²

The area of the enlarged rectangle is 30cm x 12cm = 360cm²

As you can see the area of the enlarged rectangle is 6² times larger than the area of the original rectangle.

The same can be shown for any polygon when enlarged.

Enlargement by a fractional scale factor is equivalent to the shape reducing in size.

If you enlarge the dimensions of a three dimensional shape by a scale factor, the volume is increased by the cube of that factor.

For example if the sides of a cuboid are enlarged by a factor of 6, the volume of the cuboid increases by a factor of 6³

Don't wait until you have finished the exercise before you click on the 'Check' button. Click it often as you work through the questions to see if you are answering them correctly.

1. The statue of a cat is 88cm tall which is four times bigger than the actual cat which was used as the model. How tall is the real cat?	Working: cm
2. A rectangle has an area of 19cm². A second rectangle is similar to the first but its dimensions are two times bigger. What is the area of the second rectangle?	Working: cm²
3. A box has a surface area of 600cm². A second box is 2 times as wide,2 times as long and 2 times as tall. What is the surface area of the second box?	Working: cm²
4. The smaller box shown above has a volume of 1000cm³. What is the volume of the second box given that its dimensions are twice the first box's?	Working: cm³
5. The volume of a large bottle of wine is 1200ml. A minature bottle is similar to the large bottle but its dimensions are two times smaller. What is the volume of the smaller bottle?	Working: ml
6. The area of a piece of land is 47.32m². The same piece of land is shown on a map by an area of 28cm². How long would a footpath be if on the map it is 15cm long?	Working: m
7. A real bus is fourteen times as long as a model which was used in the design process. All of the other dimensions are in proportion. The area of the glass in the windows of the model is 2m². What is the area of the glass in the real bus?	Working: m²
8. The capacity of the fuel tank of the real bus mentioned above is 49392cc. What is the capacity of the fuel tank on the model?	Working: cc
9. The model bus has five tyres (including the spare). How many tyres does the real bus have?	Working: tyres
10. In a triangle ABC, D is a point on the line AC and E is a point on the line AB. A straight line connects D and E and is parallel to CB. Sketch the diagram and mark the following lengths: DE is 4cm, AE is 1cm longer than DE, DC is 1cm shorter than DE, CB is 4cm longer than DC. The two triangles in the diagram are similar. What is area of the larger triangle (to the nearest whole number of square centimetres) if the area of the smaller triangle is 7.81cm²?	Working: cm²

Similar Shapes

Questions about the scale factors of lengths, areas and volumes of similar shapes.

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Instructions

More Activities:

Featured Activity

Three Ways

Answers

Go Maths

Maths Map

Teachers

Description of Levels

Curriculum Reference

Help

Enlargements

Don't wait until you have finished the exercise before you click on the 'Check' button. Click it often as you work through the questions to see if you are answering them correctly.