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Understanding Mathematical Similarity
Similar shapes are identical in form but different in size - think of it like zooming in or out on your phone camera. The key is recognising that one shape is simply an enlargement of another.
You'll face two main types of similarity questions in your exams. First are the straightforward "find the missing measurement" problems, and second are worded questions that require you to spot the similarity yourself.
The secret weapon for tackling these problems is working out your scale factors first. You need three different ones: LSF (length scale factor in cm), ASF (area scale factor in cm²), and VSF (volume scale factor in cm³).
Quick Tip: If your calculator gives you a long decimal, it's often better to leave your answer as a fraction - it's usually more accurate!
Working with Scale Factors
When you've got similar shapes, finding the length scale factor (LSF) is your starting point. Simply divide the larger measurement by the smaller one (or vice versa if you're going the other way).
Once you've got your LSF, everything else follows a pattern. The area scale factor (ASF) is always LSF squared, whilst the volume scale factor (VSF) is LSF cubed.
Let's say your LSF is 4. This means lengths multiply by 4, areas multiply by 16 (4²), and volumes multiply by 64 (4³). It's like a mathematical domino effect.
Remember: When you're finding missing lengths, multiply or divide by the LSF. For areas, use the ASF. For volumes, use the VSF.
Solving Real Similarity Problems
Practice makes perfect with similarity problems, and the method stays consistent. Start by identifying corresponding sides to find your scale factor, then apply it correctly.
In triangle problems, match up the sides carefully - AB corresponds to DE, BC to EF, and so on. Once you've calculated your LSF, you can find any missing length by multiplying or dividing appropriately.
Worded problems often disguise similarity - like the monster toy example where a 20cm monster becomes 120cm. The LSF here is 6, making the ASF equal to 36, so the surface area increases dramatically from 300cm² to 10,800cm².
Pro Strategy: Always write down your scale factors clearly at the start - it prevents mistakes and shows your working to earn marks.
Tackling Complex 3D Problems
Prisms and 3D shapes follow the same similarity rules, but you need to be extra careful with your calculations. The volume of a prism equals cross-sectional area times length.
When dealing with similar prisms, remember that if the cross-sections are similar, the whole prisms are similar too. Work out your LSF from corresponding edges, then cube it to get your VSF.
In complex problems, break everything down into steps. Calculate the original volume first, then multiply by your VSF to find the similar shape's volume. The prism example shows this perfectly - 150cm³ becomes 1200cm³ when the VSF is 8.
Success Tip: Double-check your scale factor calculation - most mistakes happen here, not in the final multiplication or division.
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The app is very easy to use and well designed. I have found everything I was looking for so far and have been able to learn a lot from the presentations! I will definitely use the app for a class assignment! And of course it also helps a lot as an inspiration.
Stefan S
iOS user
This app is really great. There are so many study notes and help [...]. My problem subject is French, for example, and the app has so many options for help. Thanks to this app, I have improved my French. I would recommend it to anyone.
Samantha Klich
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Wow, I am really amazed. I just tried the app because I've seen it advertised many times and was absolutely stunned. This app is THE HELP you want for school and above all, it offers so many things, such as workouts and fact sheets, which have been VERY helpful to me personally.
Anna
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Best app on earth! no words because it’s too good
Thomas R
iOS user
Just amazing. Let's me revise 10x better, this app is a quick 10/10. I highly recommend it to anyone. I can watch and search for notes. I can save them in the subject folder. I can revise it any time when I come back. If you haven't tried this app, you're really missing out.
Basil
Android user
This app has made me feel so much more confident in my exam prep, not only through boosting my own self confidence through the features that allow you to connect with others and feel less alone, but also through the way the app itself is centred around making you feel better. It is easy to navigate, fun to use, and helpful to anyone struggling in absolutely any way.
David K
iOS user
The app's just great! All I have to do is enter the topic in the search bar and I get the response real fast. I don't have to watch 10 YouTube videos to understand something, so I'm saving my time. Highly recommended!
Sudenaz Ocak
Android user
In school I was really bad at maths but thanks to the app, I am doing better now. I am so grateful that you made the app.
Greenlight Bonnie
Android user
very reliable app to help and grow your ideas of Maths, English and other related topics in your works. please use this app if your struggling in areas, this app is key for that. wish I'd of done a review before. and it's also free so don't worry about that.
Rohan U
Android user
I know a lot of apps use fake accounts to boost their reviews but this app deserves it all. Originally I was getting 4 in my English exams and this time I got a grade 7. I didn’t even know about this app three days until the exam and it has helped A LOT. Please actually trust me and use it as I’m sure you too will see developments.
Xander S
iOS user
THE QUIZES AND FLASHCARDS ARE SO USEFUL AND I LOVE THE SCHOOLGPT. IT ALSO IS LITREALLY LIKE CHATGPT BUT SMARTER!! HELPED ME WITH MY MASCARA PROBLEMS TOO!! AS WELL AS MY REAL SUBJECTS ! DUHHH 😍😁😲🤑💗✨🎀😮
Elisha
iOS user
This apps acc the goat. I find revision so boring but this app makes it so easy to organize it all and then you can ask the freeeee ai to test yourself so good and you can easily upload your own stuff. highly recommend as someone taking mocks now
Paul T
iOS user
The app is very easy to use and well designed. I have found everything I was looking for so far and have been able to learn a lot from the presentations! I will definitely use the app for a class assignment! And of course it also helps a lot as an inspiration.
Stefan S
iOS user
This app is really great. There are so many study notes and help [...]. My problem subject is French, for example, and the app has so many options for help. Thanks to this app, I have improved my French. I would recommend it to anyone.
Samantha Klich
Android user
Wow, I am really amazed. I just tried the app because I've seen it advertised many times and was absolutely stunned. This app is THE HELP you want for school and above all, it offers so many things, such as workouts and fact sheets, which have been VERY helpful to me personally.
Anna
iOS user
Best app on earth! no words because it’s too good
Thomas R
iOS user
Just amazing. Let's me revise 10x better, this app is a quick 10/10. I highly recommend it to anyone. I can watch and search for notes. I can save them in the subject folder. I can revise it any time when I come back. If you haven't tried this app, you're really missing out.
Basil
Android user
This app has made me feel so much more confident in my exam prep, not only through boosting my own self confidence through the features that allow you to connect with others and feel less alone, but also through the way the app itself is centred around making you feel better. It is easy to navigate, fun to use, and helpful to anyone struggling in absolutely any way.
David K
iOS user
The app's just great! All I have to do is enter the topic in the search bar and I get the response real fast. I don't have to watch 10 YouTube videos to understand something, so I'm saving my time. Highly recommended!
Sudenaz Ocak
Android user
In school I was really bad at maths but thanks to the app, I am doing better now. I am so grateful that you made the app.
Greenlight Bonnie
Android user
very reliable app to help and grow your ideas of Maths, English and other related topics in your works. please use this app if your struggling in areas, this app is key for that. wish I'd of done a review before. and it's also free so don't worry about that.
Rohan U
Android user
I know a lot of apps use fake accounts to boost their reviews but this app deserves it all. Originally I was getting 4 in my English exams and this time I got a grade 7. I didn’t even know about this app three days until the exam and it has helped A LOT. Please actually trust me and use it as I’m sure you too will see developments.
Xander S
iOS user
THE QUIZES AND FLASHCARDS ARE SO USEFUL AND I LOVE THE SCHOOLGPT. IT ALSO IS LITREALLY LIKE CHATGPT BUT SMARTER!! HELPED ME WITH MY MASCARA PROBLEMS TOO!! AS WELL AS MY REAL SUBJECTS ! DUHHH 😍😁😲🤑💗✨🎀😮
Elisha
iOS user
This apps acc the goat. I find revision so boring but this app makes it so easy to organize it all and then you can ask the freeeee ai to test yourself so good and you can easily upload your own stuff. highly recommend as someone taking mocks now
Paul T
iOS user
Understanding Similarity for GCSE Mathematics
Similar shapes in maths are like having a photo that's been resized - they're exactly the same shape but different sizes. One shape is simply an enlargement of another, and understanding this concept will help you tackle missing length, area,... Show more
Understanding Mathematical Similarity
Similar shapes are identical in form but different in size - think of it like zooming in or out on your phone camera. The key is recognising that one shape is simply an enlargement of another.
You'll face two main types of similarity questions in your exams. First are the straightforward "find the missing measurement" problems, and second are worded questions that require you to spot the similarity yourself.
The secret weapon for tackling these problems is working out your scale factors first. You need three different ones: LSF (length scale factor in cm), ASF (area scale factor in cm²), and VSF (volume scale factor in cm³).
Quick Tip: If your calculator gives you a long decimal, it's often better to leave your answer as a fraction - it's usually more accurate!
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Improve your grades
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By signing up you accept Terms of Service and Privacy Policy
Working with Scale Factors
When you've got similar shapes, finding the length scale factor (LSF) is your starting point. Simply divide the larger measurement by the smaller one (or vice versa if you're going the other way).
Once you've got your LSF, everything else follows a pattern. The area scale factor (ASF) is always LSF squared, whilst the volume scale factor (VSF) is LSF cubed.
Let's say your LSF is 4. This means lengths multiply by 4, areas multiply by 16 (4²), and volumes multiply by 64 (4³). It's like a mathematical domino effect.
Remember: When you're finding missing lengths, multiply or divide by the LSF. For areas, use the ASF. For volumes, use the VSF.
Sign up to see the contentIt's free!
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Improve your grades
Join milions of students
By signing up you accept Terms of Service and Privacy Policy
Solving Real Similarity Problems
Practice makes perfect with similarity problems, and the method stays consistent. Start by identifying corresponding sides to find your scale factor, then apply it correctly.
In triangle problems, match up the sides carefully - AB corresponds to DE, BC to EF, and so on. Once you've calculated your LSF, you can find any missing length by multiplying or dividing appropriately.
Worded problems often disguise similarity - like the monster toy example where a 20cm monster becomes 120cm. The LSF here is 6, making the ASF equal to 36, so the surface area increases dramatically from 300cm² to 10,800cm².
Pro Strategy: Always write down your scale factors clearly at the start - it prevents mistakes and shows your working to earn marks.
Sign up to see the contentIt's free!
Access to all documents
Improve your grades
Join milions of students
By signing up you accept Terms of Service and Privacy Policy
Tackling Complex 3D Problems
Prisms and 3D shapes follow the same similarity rules, but you need to be extra careful with your calculations. The volume of a prism equals cross-sectional area times length.
When dealing with similar prisms, remember that if the cross-sections are similar, the whole prisms are similar too. Work out your LSF from corresponding edges, then cube it to get your VSF.
In complex problems, break everything down into steps. Calculate the original volume first, then multiply by your VSF to find the similar shape's volume. The prism example shows this perfectly - 150cm³ becomes 1200cm³ when the VSF is 8.
Success Tip: Double-check your scale factor calculation - most mistakes happen here, not in the final multiplication or division.
We thought you’d never ask...
What is the Knowunity AI companion?
Our AI Companion is a student-focused AI tool that offers more than just answers. Built on millions of Knowunity resources, it provides relevant information, personalised study plans, quizzes, and content directly in the chat, adapting to your individual learning journey.
Where can I download the Knowunity app?
You can download the app from Google Play Store and Apple App Store.
Is Knowunity really free of charge?
That's right! Enjoy free access to study content, connect with fellow students, and get instant help – all at your fingertips.
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Most popular content in Maths
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Can't find what you're looking for? Explore other subjects.
Students love us — and so will you.
4.9/5
App Store
4.8/5
Google Play
The app is very easy to use and well designed. I have found everything I was looking for so far and have been able to learn a lot from the presentations! I will definitely use the app for a class assignment! And of course it also helps a lot as an inspiration.
Stefan S
iOS user
This app is really great. There are so many study notes and help [...]. My problem subject is French, for example, and the app has so many options for help. Thanks to this app, I have improved my French. I would recommend it to anyone.
Samantha Klich
Android user
Wow, I am really amazed. I just tried the app because I've seen it advertised many times and was absolutely stunned. This app is THE HELP you want for school and above all, it offers so many things, such as workouts and fact sheets, which have been VERY helpful to me personally.
Anna
iOS user
Best app on earth! no words because it’s too good
Thomas R
iOS user
Just amazing. Let's me revise 10x better, this app is a quick 10/10. I highly recommend it to anyone. I can watch and search for notes. I can save them in the subject folder. I can revise it any time when I come back. If you haven't tried this app, you're really missing out.
Basil
Android user
This app has made me feel so much more confident in my exam prep, not only through boosting my own self confidence through the features that allow you to connect with others and feel less alone, but also through the way the app itself is centred around making you feel better. It is easy to navigate, fun to use, and helpful to anyone struggling in absolutely any way.
David K
iOS user
The app's just great! All I have to do is enter the topic in the search bar and I get the response real fast. I don't have to watch 10 YouTube videos to understand something, so I'm saving my time. Highly recommended!
Sudenaz Ocak
Android user
In school I was really bad at maths but thanks to the app, I am doing better now. I am so grateful that you made the app.
Greenlight Bonnie
Android user
very reliable app to help and grow your ideas of Maths, English and other related topics in your works. please use this app if your struggling in areas, this app is key for that. wish I'd of done a review before. and it's also free so don't worry about that.
Rohan U
Android user
I know a lot of apps use fake accounts to boost their reviews but this app deserves it all. Originally I was getting 4 in my English exams and this time I got a grade 7. I didn’t even know about this app three days until the exam and it has helped A LOT. Please actually trust me and use it as I’m sure you too will see developments.
Xander S
iOS user
THE QUIZES AND FLASHCARDS ARE SO USEFUL AND I LOVE THE SCHOOLGPT. IT ALSO IS LITREALLY LIKE CHATGPT BUT SMARTER!! HELPED ME WITH MY MASCARA PROBLEMS TOO!! AS WELL AS MY REAL SUBJECTS ! DUHHH 😍😁😲🤑💗✨🎀😮
Elisha
iOS user
This apps acc the goat. I find revision so boring but this app makes it so easy to organize it all and then you can ask the freeeee ai to test yourself so good and you can easily upload your own stuff. highly recommend as someone taking mocks now
Paul T
iOS user
The app is very easy to use and well designed. I have found everything I was looking for so far and have been able to learn a lot from the presentations! I will definitely use the app for a class assignment! And of course it also helps a lot as an inspiration.
Stefan S
iOS user
This app is really great. There are so many study notes and help [...]. My problem subject is French, for example, and the app has so many options for help. Thanks to this app, I have improved my French. I would recommend it to anyone.
Samantha Klich
Android user
Wow, I am really amazed. I just tried the app because I've seen it advertised many times and was absolutely stunned. This app is THE HELP you want for school and above all, it offers so many things, such as workouts and fact sheets, which have been VERY helpful to me personally.
Anna
iOS user
Best app on earth! no words because it’s too good
Thomas R
iOS user
Just amazing. Let's me revise 10x better, this app is a quick 10/10. I highly recommend it to anyone. I can watch and search for notes. I can save them in the subject folder. I can revise it any time when I come back. If you haven't tried this app, you're really missing out.
Basil
Android user
This app has made me feel so much more confident in my exam prep, not only through boosting my own self confidence through the features that allow you to connect with others and feel less alone, but also through the way the app itself is centred around making you feel better. It is easy to navigate, fun to use, and helpful to anyone struggling in absolutely any way.
David K
iOS user
The app's just great! All I have to do is enter the topic in the search bar and I get the response real fast. I don't have to watch 10 YouTube videos to understand something, so I'm saving my time. Highly recommended!
Sudenaz Ocak
Android user
In school I was really bad at maths but thanks to the app, I am doing better now. I am so grateful that you made the app.
Greenlight Bonnie
Android user
very reliable app to help and grow your ideas of Maths, English and other related topics in your works. please use this app if your struggling in areas, this app is key for that. wish I'd of done a review before. and it's also free so don't worry about that.
Rohan U
Android user
I know a lot of apps use fake accounts to boost their reviews but this app deserves it all. Originally I was getting 4 in my English exams and this time I got a grade 7. I didn’t even know about this app three days until the exam and it has helped A LOT. Please actually trust me and use it as I’m sure you too will see developments.
Xander S
iOS user
THE QUIZES AND FLASHCARDS ARE SO USEFUL AND I LOVE THE SCHOOLGPT. IT ALSO IS LITREALLY LIKE CHATGPT BUT SMARTER!! HELPED ME WITH MY MASCARA PROBLEMS TOO!! AS WELL AS MY REAL SUBJECTS ! DUHHH 😍😁😲🤑💗✨🎀😮
Elisha
iOS user
This apps acc the goat. I find revision so boring but this app makes it so easy to organize it all and then you can ask the freeeee ai to test yourself so good and you can easily upload your own stuff. highly recommend as someone taking mocks now
Paul T
iOS user