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Organisms respond to changes in their internal and external environments (a-level only)
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Britain & the wider world: 1745 -1901
1l the quest for political stability: germany, 1871-1991
The cold war
Inter-war germany
Medieval period: 1066 -1509
2d religious conflict and the church in england, c1529-c1570
2o democracy and nazism: germany, 1918-1945
1f industrialisation and the people: britain, c1783-1885
1c the tudors: england, 1485-1603
2m wars and welfare: britain in transition, 1906-1957
World war two & the holocaust
2n revolution and dictatorship: russia, 1917-1953
2s the making of modern britain, 1951-2007
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Maths
12 Dec 2025
173
2 pages
Triangles are everywhere in maths, and understanding their properties and how to calculate their area is essential for... Show more
Every triangle you'll ever encounter has one thing in common all three angles add up to 180 degrees. This is a fundamental rule that never changes, no matter what type of triangle you're working with.
There are three main types of triangles you need to know. An equilateral triangle is the most symmetrical - all three sides are exactly the same length, and all three angles are 60 degrees each.
A scalene triangle is like the rebel of the triangle family - every side is a different length, and every angle is different too. Most triangles you see in real life are scalene triangles.
Isosceles triangles are the compromise between the two - they have exactly two equal sides and two equal angles, with the third side and angle being different.
Quick Check Remember that no matter which type you're dealing with, those three angles will always add up to 180 degrees!
Here's the brilliant news there's just one formula for finding the area of any triangle, regardless of whether it's equilateral, scalene, or isosceles. The triangle area formula is Area = ยฝ ร base ร height.
You can write this formula in different ways - some people prefer base ร height รท 2, which gives exactly the same answer. The key is identifying your base (any side of the triangle) and the height (the perpendicular distance from that base to the opposite corner).
The height is crucial - it must be measured at a right angle to the base you've chosen. Don't just use any side length as the height, as this will give you the wrong answer.
Top Tip Always double-check that your height measurement forms a 90-degree angle with your chosen base - this is where most mistakes happen!
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.
You can download the app from Google Play Store and Apple App Store.
That's right! Enjoy free access to study content, connect with fellow students, and get instant help โ all at your fingertips.
6
Smart Tools NEW
Transform this note into: โ 50+ Practice Questions โ Interactive Flashcards โ Full Mock Exam โ Essay Outlines
Enhance your exam readiness with this comprehensive practice paper for the Edexcel Level 1/Level 2 GCSE (9-1) Mathematics Higher Tier. This resource includes answered questions covering key concepts such as trigonometry, probability, statistics, and geometry. Ideal for students preparing for their GCSE exams, this paper helps reinforce understanding and application of mathematical principles.
MathsExplore essential GCSE maths formulas including area, volume, trigonometry, and probability. This comprehensive summary covers key concepts such as the Pythagorean theorem, sine and cosine rules, and quadratic equations, making it an invaluable resource for exam preparation.
MathsPrepare for your GCSE Higher Mathematics exam with this comprehensive mock exam set. This resource covers key topics such as simplifying rational expressions, solving inequalities, geometric transformations, and more. Ideal for students looking to practice and improve their understanding of essential mathematical concepts. Includes detailed solutions and explanations for each question.
MathsComprehensive answers and explanations for GCSE Maths Paper 1, covering key concepts such as arithmetic sequences, probability, graph types, and statistical analysis. Ideal for students preparing for their exams. Includes worked examples and step-by-step solutions.
MathsExplore essential formulas for calculating the area of various geometric shapes, including triangles, trapeziums, parallelograms, and kites. This summary provides clear definitions and calculations to help you master area concepts in geometry.
MathsMaster the process of determining the Nth term in quadratic sequences through first and second differences. This summary covers essential techniques, including Nยฒ calculations and difference tables, to enhance your understanding of polynomials and sequences.
MathsApp Store
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 itโs 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 didnโt even know about this app three days until the exam and it has helped A LOT. Please actually trust me and use it as Iโm 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 ๐๐๐ฒ๐ค๐โจ๐๐ฎ
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 itโs 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 didnโt even know about this app three days until the exam and it has helped A LOT. Please actually trust me and use it as Iโm 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 ๐๐๐ฒ๐ค๐โจ๐๐ฎ
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
Triangles are everywhere in maths, and understanding their properties and how to calculate their area is essential for your GCSE studies. Let's break down the three main types of triangles and master the simple formula that works for all of... Show more
Access to all documents
Improve your grades
Join milions of students
By signing up you accept Terms of Service and Privacy Policy
Every triangle you'll ever encounter has one thing in common: all three angles add up to 180 degrees. This is a fundamental rule that never changes, no matter what type of triangle you're working with.
There are three main types of triangles you need to know. An equilateral triangle is the most symmetrical - all three sides are exactly the same length, and all three angles are 60 degrees each.
A scalene triangle is like the rebel of the triangle family - every side is a different length, and every angle is different too. Most triangles you see in real life are scalene triangles.
Isosceles triangles are the compromise between the two - they have exactly two equal sides and two equal angles, with the third side and angle being different.
Quick Check: Remember that no matter which type you're dealing with, those three angles will always add up to 180 degrees!
Access to all documents
Improve your grades
Join milions of students
By signing up you accept Terms of Service and Privacy Policy
Here's the brilliant news: there's just one formula for finding the area of any triangle, regardless of whether it's equilateral, scalene, or isosceles. The triangle area formula is: Area = ยฝ ร base ร height.
You can write this formula in different ways - some people prefer base ร height รท 2, which gives exactly the same answer. The key is identifying your base (any side of the triangle) and the height (the perpendicular distance from that base to the opposite corner).
The height is crucial - it must be measured at a right angle to the base you've chosen. Don't just use any side length as the height, as this will give you the wrong answer.
Top Tip: Always double-check that your height measurement forms a 90-degree angle with your chosen base - this is where most mistakes happen!
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.
You can download the app from Google Play Store and Apple App Store.
That's right! Enjoy free access to study content, connect with fellow students, and get instant help โ all at your fingertips.
6
Smart Tools NEW
Transform this note into: โ 50+ Practice Questions โ Interactive Flashcards โ Full Mock Exam โ Essay Outlines
Enhance your exam readiness with this comprehensive practice paper for the Edexcel Level 1/Level 2 GCSE (9-1) Mathematics Higher Tier. This resource includes answered questions covering key concepts such as trigonometry, probability, statistics, and geometry. Ideal for students preparing for their GCSE exams, this paper helps reinforce understanding and application of mathematical principles.
MathsExplore essential GCSE maths formulas including area, volume, trigonometry, and probability. This comprehensive summary covers key concepts such as the Pythagorean theorem, sine and cosine rules, and quadratic equations, making it an invaluable resource for exam preparation.
MathsPrepare for your GCSE Higher Mathematics exam with this comprehensive mock exam set. This resource covers key topics such as simplifying rational expressions, solving inequalities, geometric transformations, and more. Ideal for students looking to practice and improve their understanding of essential mathematical concepts. Includes detailed solutions and explanations for each question.
MathsComprehensive answers and explanations for GCSE Maths Paper 1, covering key concepts such as arithmetic sequences, probability, graph types, and statistical analysis. Ideal for students preparing for their exams. Includes worked examples and step-by-step solutions.
MathsExplore essential formulas for calculating the area of various geometric shapes, including triangles, trapeziums, parallelograms, and kites. This summary provides clear definitions and calculations to help you master area concepts in geometry.
MathsMaster the process of determining the Nth term in quadratic sequences through first and second differences. This summary covers essential techniques, including Nยฒ calculations and difference tables, to enhance your understanding of polynomials and sequences.
MathsApp Store
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 itโs 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 didnโt even know about this app three days until the exam and it has helped A LOT. Please actually trust me and use it as Iโm 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 ๐๐๐ฒ๐ค๐โจ๐๐ฎ
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 itโs 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 didnโt even know about this app three days until the exam and it has helped A LOT. Please actually trust me and use it as Iโm 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 ๐๐๐ฒ๐ค๐โจ๐๐ฎ
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
Sociology