Prism
A prism is a special polyhedron where a polygon of constant shape and size runs through its entire length, appearing as two identical parallel faces. In Saxon Math, Course 2, Grade 7 students identify prisms by their cross-sectional shape: a triangular prism has two triangular bases and three rectangular sides, while a rectangular prism (like a shoebox) has two rectangular bases and four rectangular sides. The type of prism is named after its base polygon. Understanding prisms is foundational for calculating surface area and volume in Grade 7 geometry.
Key Concepts
Property 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.
Examples A triangular prism has two parallel triangle faces and three rectangular side faces. A rectangular prism, like a shoebox, has two parallel rectangle faces and four other rectangular faces. To draw a triangular prism, draw two identical triangles and connect their matching corners (vertices).
Explanation 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.
Common Questions
What is a prism in Grade 7 geometry?
A prism is a three-dimensional polyhedron with two parallel, identical polygon faces (bases) connected by rectangular side faces. The shape of the base determines the name of the prism.
How do you identify the type of prism?
Look at the base — the two parallel, identical polygon faces. If the base is a triangle, it is a triangular prism. If it is a rectangle, it is a rectangular prism.
What are the parts of a prism?
A prism has two congruent, parallel bases (the polygon faces) and lateral faces (the rectangular sides connecting the bases). The number of lateral faces equals the number of sides of the base polygon.
How is a prism different from a pyramid?
A prism has two parallel bases of the same shape. A pyramid has one base and triangular faces that meet at a single apex (point).
Where are prisms taught in Saxon Math Course 2?
Prisms are introduced in Saxon Math, Course 2, as part of Grade 7 three-dimensional geometry content.
What are some real-world examples of prisms?
A shoebox is a rectangular prism, a triangular tunnel is a triangular prism, a Toblerone chocolate box is a triangular prism, and a swimming pool with a uniform cross-section is a rectangular prism.
How does understanding prisms help with volume calculations?
The volume formula V = base area × height works for all prisms because the uniform cross-section means you are simply stacking the base shape repeatedly.