Three-dimensional figures are shapes that take up space in all...
Mathematics59 views·Updated Jun 15, 2026·2 pagesMath 7: Comprehensive Notes on 3D Figures
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Three-Dimensional Figures
Ever wondered what makes a box different from a pyramid? It's all about their 3D structure! A solid is any three-dimensional figure that encloses space. The most common type is a polyhedron, which is made up of flat polygons called faces.
Where these faces meet, they form edges (line segments), and where edges meet, they create vertices (points). When you connect two vertices that aren't on the same face, you create a diagonal.
Common solids come in different shapes. Prisms have two identical bases with rectangular faces connecting them - like a rectangular box or a triangular prism. Pyramids have just one base with triangular faces that meet at a point - think of the famous pyramids in Egypt!
Fun Fact: Most everyday objects are 3D solids! Your juice box is a rectangular prism, while a party hat resembles a cone. Start noticing these shapes around you!
There are also cylinders with two circular bases, and cones with one circular base that tapers to a point. These rounded solids don't have flat polygon faces like polyhedrons do.
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Surface Area of 3D Figures
Imagine unwrapping a 3D shape completely flat - that's the surface area! It tells you how much material would cover the entire outside of the solid. This is super useful for real problems like figuring out how much wrapping paper you need.
For a rectangular prism, find the area of each of the six faces and add them up. You can group similar faces together: front/back, left/right, and top/bottom. For example, a 3×4×6 inch box has a surface area of 108 square inches.
A triangular prism requires finding the area of its two triangular bases plus its three rectangular sides. Remember that a triangle's area is ½ × base × height! For the cylinder shown, with its triangular bases and rectangular sides, the total surface area is 336 square inches.
Remember: When finding a cylinder's surface area, don't forget both circular bases AND the curved side. The curved side is basically a rectangle with width equal to the cylinder's circumference!
For a cylinder, calculate the area of its two circular bases (πr²) and add the curved surface (2πrh). For a cylinder with radius 4 inches and height 10 inches, the total surface area is about 351.68 square inches.
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Mathematics59 views·Updated Jun 15, 2026·2 pagesMath 7: Comprehensive Notes on 3D Figures
Three-dimensional figures are shapes that take up space in all directions. We'll explore different types of 3D solids and learn how to calculate their surface areas. Understanding these concepts will help you visualize and measure real-world objects like boxes, cans,...
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Three-Dimensional Figures
Ever wondered what makes a box different from a pyramid? It's all about their 3D structure! A solid is any three-dimensional figure that encloses space. The most common type is a polyhedron, which is made up of flat polygons called faces.
Where these faces meet, they form edges (line segments), and where edges meet, they create vertices (points). When you connect two vertices that aren't on the same face, you create a diagonal.
Common solids come in different shapes. Prisms have two identical bases with rectangular faces connecting them - like a rectangular box or a triangular prism. Pyramids have just one base with triangular faces that meet at a point - think of the famous pyramids in Egypt!
Fun Fact: Most everyday objects are 3D solids! Your juice box is a rectangular prism, while a party hat resembles a cone. Start noticing these shapes around you!
There are also cylinders with two circular bases, and cones with one circular base that tapers to a point. These rounded solids don't have flat polygon faces like polyhedrons do.
2
of 2Sign up to see the content. It's free!
- Access to all documents
- Improve your grades
- Join milions of students
Surface Area of 3D Figures
Imagine unwrapping a 3D shape completely flat - that's the surface area! It tells you how much material would cover the entire outside of the solid. This is super useful for real problems like figuring out how much wrapping paper you need.
For a rectangular prism, find the area of each of the six faces and add them up. You can group similar faces together: front/back, left/right, and top/bottom. For example, a 3×4×6 inch box has a surface area of 108 square inches.
A triangular prism requires finding the area of its two triangular bases plus its three rectangular sides. Remember that a triangle's area is ½ × base × height! For the cylinder shown, with its triangular bases and rectangular sides, the total surface area is 336 square inches.
Remember: When finding a cylinder's surface area, don't forget both circular bases AND the curved side. The curved side is basically a rectangle with width equal to the cylinder's circumference!
For a cylinder, calculate the area of its two circular bases (πr²) and add the curved surface (2πrh). For a cylinder with radius 4 inches and height 10 inches, the total surface area is about 351.68 square inches.
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What is the Knowunity AI companion?
Our AI companion is specifically built for the needs of students. Based on the millions of content pieces we have on the platform we can provide truly meaningful and relevant answers to students. But its not only about answers, the companion is even more about guiding students through their daily learning challenges, with personalised study plans, quizzes or content pieces in the chat and 100% personalisation based on the students skills and developments.
Where can I download the Knowunity app?
You can download the app in the Google Play Store and in the 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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Stefan SiOS 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.
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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.
AnnaiOS user