Similar ShapesQuestions about the scale factors of lengths, areas and volumes of similar shapes. 
This is level 4; Mixed questions. You can earn a trophy if you get at least 7 questions correct.
InstructionsTry 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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Mathematicians are not the people who find Maths easy; they are the people who enjoy how mystifying, puzzling and hard it is. Are you a mathematician? Comment recorded on the 14 October 'Starter of the Day' page by Inger Kisby, Herts and Essex High School: "Just a quick note to say that we use a lot of your starters. It is lovely to have so many different ideas to start a lesson with. Thank you very much and keep up the good work." Comment recorded on the 19 November 'Starter of the Day' page by Lesley Sewell, Ysgol Aberconwy, Wales: "A Maths colleague introduced me to your web site and I love to use it. The questions are so varied I can use them with all of my classes, I even let year 13 have a go at some of them. I like being able to access the whole month so I can use favourites with classes I see at different times of the week. Thanks." 


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Go MathsLearning and understanding Mathematics, at every level, requires learner engagement. Mathematics is not a spectator sport. Sometimes traditional teaching fails to actively involve students. One way to address the problem is through the use of interactive activities and this web site provides many of those. The Go Maths page is an alphabetical list of free activities designed for students in Secondary/High school. Maths MapAre you looking for something specific? An exercise to supplement the topic you are studying at school at the moment perhaps. Navigate using our Maths Map to find exercises, puzzles and Maths lesson starters grouped by topic. TeachersIf you found this activity useful don't forget to record it in your scheme of work or learning management system. The short URL, ready to be copied and pasted, is as follows: 

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Level 1  Lengths of similar shapes
Level 2  Areas of similar shapes
Level 3  Volumes of similar shapes
Level 4  Mixed questions
Level 5  Examstyle questions
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 6^{2}
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 = 10cm^{2}
The area of the enlarged rectangle is 30cm x 12cm = 360cm^{2}
As you can see the area of the enlarged rectangle is 6^{2} 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 6^{3}
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