A prism is a three-dimensional solid with two parallel, congruent bases connected by flat side faces. Prisms are important because they model many real objects, such as boxes, buildings, crystals, and packaging. Learning prisms helps students connect 2D geometry to 3D measurement.
The main ideas are base shape, height, surface area, and volume.
A prism is named by the shape of its bases, such as triangular prism, rectangular prism, or hexagonal prism. In a right prism, the side faces are rectangles and the height is perpendicular to the bases. In an oblique prism, the bases are still parallel and congruent, but the side faces slant and the height must be measured along a perpendicular line.
The volume of any prism depends on the area of one base and the perpendicular height between the bases.
Key Facts
- A prism has two parallel congruent bases and side faces that are parallelograms.
- A right prism has lateral edges perpendicular to the bases, so its side faces are rectangles.
- An oblique prism is slanted, but its bases are still parallel and congruent.
- Prisms are named by their base shape, such as triangular prism or rectangular prism.
- Volume of any prism: V = Bh, where B is the area of one base and h is the perpendicular height.
- Surface area of a right prism: SA = 2B + Ph, where P is the perimeter of the base.
Vocabulary
- Prism
- A prism is a solid with two parallel congruent bases connected by flat side faces.
- Base
- A base is one of the two parallel congruent faces that give a prism its name.
- Lateral face
- A lateral face is a side face that connects corresponding edges of the two bases.
- Height
- The height of a prism is the perpendicular distance between its two bases.
- Right prism
- A right prism is a prism whose lateral edges are perpendicular to the bases.
Common Mistakes to Avoid
- Using a slanted edge as the height, which is wrong because height must be the perpendicular distance between the bases.
- Counting all faces as bases, which is wrong because only the two parallel congruent faces are the bases.
- Naming a prism by a side face, which is wrong because a prism is named by the shape of its base.
- Using V = lwh for every prism, which is wrong because that formula only directly fits rectangular prisms and the general formula is V = Bh.
Practice Questions
- 1 A right rectangular prism has length 8 cm, width 5 cm, and height 12 cm. Find its volume and total surface area.
- 2 A right triangular prism has a triangular base with base 10 m and height 6 m. The prism height is 15 m. Find the volume of the prism.
- 3 An oblique prism and a right prism have congruent bases and the same perpendicular height. Explain why their volumes are equal even though one is slanted.