In Saxon Math Course 2, Grade 7 Lesson 67 introduces students to geometric solids, including spheres, cylinders, cones, prisms, and pyramids. Students learn to distinguish polyhedrons from solids with curved surfaces and identify the faces, edges, and vertices of figures like cubes and triangular prisms. The lesson also covers how three-dimensional figures are formed by moving two-dimensional shapes through space and how nets represent unfolded solids.
Section 1
📘 Geometric Solids
Geometric solids are shapes that take up space. A solid with only flat, polygon surfaces is a polyhedron, which has faces (surfaces), edges (intersections), and vertices (corners).
This is your introduction to the topic. Next, you'll tackle worked examples on identifying different solids, counting their parts, and finding the surface area of a cube.
Section 2
Polyhedron
If a solid has only flat surfaces that are polygons, the solid is called a polyhedron.
Think of a polyhedron as a 3D shape built entirely from flat puzzle pieces, like triangles or squares. Unlike a smooth, curvy basketball (a sphere), polyhedrons have sharp corners and straight edges. If you can build it with paper polygons without any bending or curving, you've probably made a polyhedron! Cubes and pyramids are perfect examples.
Section 3
Prism
A prism is a special kind of polyhedron. A prism has a polygon of a constant size running through it that appears at two opposite, parallel faces.
Imagine taking a flat shape, like a triangle, and stretching it out into 3D! That's a prism. It has two identical, parallel faces called 'bases,' and its name comes from the shape of these bases. A triangular prism has triangle bases, and a rectangular prism (like a juice box) has rectangle bases. It’s consistent through and through.
Section 4
Surface Area
The surface area of a solid is the total area of all its faces combined.
To find the surface area, imagine you're a master gift-wrapper! You need to calculate the area of paper needed to cover every single face of a 3D shape with no overlap. Just find the area of each flat face one-by-one, then add all those areas together for the grand total. It's the ultimate 'area' challenge!
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Section 1
📘 Geometric Solids
Geometric solids are shapes that take up space. A solid with only flat, polygon surfaces is a polyhedron, which has faces (surfaces), edges (intersections), and vertices (corners).
This is your introduction to the topic. Next, you'll tackle worked examples on identifying different solids, counting their parts, and finding the surface area of a cube.
Section 2
Polyhedron
If a solid has only flat surfaces that are polygons, the solid is called a polyhedron.
Think of a polyhedron as a 3D shape built entirely from flat puzzle pieces, like triangles or squares. Unlike a smooth, curvy basketball (a sphere), polyhedrons have sharp corners and straight edges. If you can build it with paper polygons without any bending or curving, you've probably made a polyhedron! Cubes and pyramids are perfect examples.
Section 3
Prism
A prism is a special kind of polyhedron. A prism has a polygon of a constant size running through it that appears at two opposite, parallel faces.
Imagine taking a flat shape, like a triangle, and stretching it out into 3D! That's a prism. It has two identical, parallel faces called 'bases,' and its name comes from the shape of these bases. A triangular prism has triangle bases, and a rectangular prism (like a juice box) has rectangle bases. It’s consistent through and through.
Section 4
Surface Area
The surface area of a solid is the total area of all its faces combined.
To find the surface area, imagine you're a master gift-wrapper! You need to calculate the area of paper needed to cover every single face of a 3D shape with no overlap. Just find the area of each flat face one-by-one, then add all those areas together for the grand total. It's the ultimate 'area' challenge!
Book overview
Jump across lessons in the current chapter without opening the full course modal.
Continue this chapter