14.2 - Prisms
Links and useful resources
- gr10's Geometry >>>START HERE<<<
- AoPS Online Textbook
- AoPS Alcumus
- Big Ideas Geometry textbook
- GeoGebra Online Geometry Constuction Tool
- Two-column math templates
- Proofs unit slides from mathgiraffe.com
- Proofs unit printables for two-column proofs
Concept summary and connections
- A prism has two congruent parallel faces, and parallelograms for all other faces.
- Surface area of a prism
- Volume of a prism
- Think of a stack of pennies...
- diagonal: A line drawn through two vertices that are not connected by an edge.
- Space diagonal: a diagonal through a prism that does NOT stay within a face.
- Face diagonal: A diagonal in a prism that stays within a face.
Prisms
A prism is a 3-dimensional figure that has:
- Two parallel, congruent faces
- parallelograms for all other faces
There are a lot of constraints among the faces of a prism that will help you find the dimensions you need (shared edges mostly).
Special prisms
- Rectangular: Every face of the prism is a rectangle
- Right: The bases are perpendicular to the non-base faces.
- Regular: the bases are regular polygons
Computing the surface area amounts to computing the area of each face and adding them together.
To compute the volume of a prism:
- Find the area of one of the parallel faces
- Find the perpendicular distance between the parallel faces
- Multiply the area by the height.
Think of a prism as a stack of pennies - shifting them around while maintaining their stacked relationship doesn't have any effect on their volume - all that matters is the volume of each penny and the height of the stack. If you make the pennies thinner, it takes more of them but their individual volumes shrink by exactly the same amount, until eventually you get to infinitesimal slices of the prism that are stacked like sheets of paper. Again, you can skew the stack any way you want without changing its volume.
Media resources
- Youtube search for "A prism has two congruent parallel faces, and parallelograms for all other faces."
- Youtube search for "Surface area of a prism"
- Youtube search for "Volume of a prism"
- Youtube search for "Think of a stack of pennies..."