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10 Dec 2025

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Area and Volume Formulas - Mathematics Guide

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ava! ๐ŸŽ€ @avaxmegan

Mastering area and volume formulas is absolutely crucial for your GCSE maths success. These handy formulas pop up... Show more

area Formulas

Square base height

rectangle base height

triangle base Perpendicular height 2

trapezium Ca+b) height 2

Parallelogram base

Essential Area and Volume Formulas

Area formulas help you calculate the space inside 2D shapes, whilst volume formulas work out how much space 3D objects take up. Think of area as the amount of wrapping paper you'd need, and volume as how much stuff you can actually fit inside!

For 2D shapes, the key ones you'll use are squares (base ร— height), rectangles (base ร— height), and triangles (base ร— perpendicular height รท 2). The trapezium formula uses a+ba+b ร— height รท 2, where a and b are the parallel sides.

Parallelograms need base ร— perpendicular height, while a rhombus uses length ร— height รท 2. For circles, it's simply ฯ€ ร— rยฒ - probably the most famous formula you'll ever learn!

Top Tip Always double-check you're using perpendicular height, not slanted height - this catches loads of students out in exams!

The 3D volume formulas follow similar patterns. Spheres use 4/3 ร— ฯ€ ร— rยณ, whilst cylinders are ฯ€ ร— rยฒ ร— height. Rectangular prisms are just length ร— width ร— height, and cones are 1/3 ร— ฯ€ ร— rยฒ ร— height. Remember that prisms multiply the base area by height, making calculations much simpler once you've got the base sorted.

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Anna

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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

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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 didnโ€™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 Iโ€™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 ๐Ÿ˜๐Ÿ˜๐Ÿ˜ฒ๐Ÿค‘๐Ÿ’—โœจ๐ŸŽ€๐Ÿ˜ฎ

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

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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

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 itโ€™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 didnโ€™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 Iโ€™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 ๐Ÿ˜๐Ÿ˜๐Ÿ˜ฒ๐Ÿค‘๐Ÿ’—โœจ๐ŸŽ€๐Ÿ˜ฎ

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

ย 

Maths

โ€ข

122

โ€ข

10 Dec 2025

โ€ข

1 page

Area and Volume Formulas - Mathematics Guide

user profile picture

ava! ๐ŸŽ€

@avaxmegan

Mastering area and volume formulas is absolutely crucial for your GCSE maths success. These handy formulas pop up everywhere - from calculating how much paint you need for your bedroom walls to working out storage space in containers.

area Formulas

Square base height

rectangle base height

triangle base Perpendicular height 2

trapezium Ca+b) height 2

Parallelogram base

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Essential Area and Volume Formulas

Area formulas help you calculate the space inside 2D shapes, whilst volume formulas work out how much space 3D objects take up. Think of area as the amount of wrapping paper you'd need, and volume as how much stuff you can actually fit inside!

For 2D shapes, the key ones you'll use are squares (base ร— height), rectangles (base ร— height), and triangles (base ร— perpendicular height รท 2). The trapezium formula uses a+ba+b ร— height รท 2, where a and b are the parallel sides.

Parallelograms need base ร— perpendicular height, while a rhombus uses length ร— height รท 2. For circles, it's simply ฯ€ ร— rยฒ - probably the most famous formula you'll ever learn!

Top Tip: Always double-check you're using perpendicular height, not slanted height - this catches loads of students out in exams!

The 3D volume formulas follow similar patterns. Spheres use 4/3 ร— ฯ€ ร— rยณ, whilst cylinders are ฯ€ ร— rยฒ ร— height. Rectangular prisms are just length ร— width ร— height, and cones are 1/3 ร— ฯ€ ร— rยฒ ร— height. Remember that prisms multiply the base area by height, making calculations much simpler once you've got the base sorted.

We thought youโ€™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 โ€“ all at your fingertips.

2

Smart Tools NEW

Transform this note into: โœ“ 50+ Practice Questions โœ“ Interactive Flashcards โœ“ Full Mock Exam โœ“ Essay Outlines

Mock Exam
Quiz
Flashcards
Essay

Similar content

GCSE maths definition and vocabulary

maths revisions

MathsMaths
11

GCSE Maths Overview

Explore the comprehensive Edexcel GCSE (9-1) Mathematics specification, covering key areas such as Number, Algebra, Geometry, and Statistics. This resource provides essential insights into assessment objectives, content weightings, and the skills required for success in both Foundation and Higher tiers. Perfect for students preparing for their exams.

MathsMaths
9

Cambridge IGCSE Maths 2025-2027

Explore the comprehensive Cambridge IGCSE Mathematics syllabus for 2025, 2026, and 2027. This guide covers key topics, assessment objectives, and the benefits of choosing this internationally recognized qualification. Ideal for students preparing for their exams, it provides insights into the curriculum structure, essential mathematical techniques, and the skills needed for further studies. Type: Syllabus Overview.

MathsMaths
11

Comprehensive Maths Concepts

Explore essential mathematical concepts including powers, geometry, statistics, and probability. This resource features 65 pages of detailed explanations, diagrams, and examples to enhance your understanding of topics such as right triangles, volume calculations, and data representation. Ideal for students seeking to strengthen their numeracy skills and grasp complex mathematical principles.

MathsMaths
10

Circle Equation Fundamentals

Explore the essential concepts of circle equations in coordinate geometry. This summary covers the standard form of a circle, how to find the center and radius, and the process of completing the square. Ideal for AQA A Level Maths students looking to master circle equations and their applications.

MathsMaths
12

Cylinder & Prism Volumes

Explore the formulas and calculations for determining the volumes of cylinders and triangular prisms. This summary includes step-by-step examples, key formulas, and problem-solving techniques essential for mastering volume calculations in geometry.

MathsMaths
8

Most popular content in Maths

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English - inspector calls quotes and analysis

Quotes from every main character

English LiteratureEnglish Literature
10

Can't find what you're looking for? Explore other subjects.

Students love us โ€” 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 itโ€™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 didnโ€™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 Iโ€™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 ๐Ÿ˜๐Ÿ˜๐Ÿ˜ฒ๐Ÿค‘๐Ÿ’—โœจ๐ŸŽ€๐Ÿ˜ฎ

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 itโ€™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 didnโ€™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 Iโ€™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 ๐Ÿ˜๐Ÿ˜๐Ÿ˜ฒ๐Ÿค‘๐Ÿ’—โœจ๐ŸŽ€๐Ÿ˜ฎ

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