Pyramids and Prisms
A Guide to Definitions, Types, and Examples
Pyramids
Definition
A pyramid is a three-dimensional polyhedron with a single polygonal base and triangular faces that converge at a point called the apex. The base can be any polygon (e.g., triangle, square, pentagon), and the number of triangular faces equals the number of sides of the base.
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Types of Pyramids
Triangular Pyramid (Tetrahedron)
Base: Triangle (3 sides)
Faces: 4 triangular faces
Square Pyramid
Base: Square (4 sides)
Faces: 4 triangular faces + 1 square base
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Hexagonal Pyramid
Base: Hexagon (6 sides)
Faces: 6 triangular faces + 1 pentagonal base
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Example
The Great Pyramid of Giza is a square pyramid with a square base. Each side of the base is approximately 230.4 meters long, and its original height was about 146.5 meters. Volume: Volume = (1/3) × Base Area × Height = (1/3) × (230.4 × 230.4) × 146.5 ≈ 2,583,283 m³.
Prisms
Definition
A prism is a three-dimensional polyhedron with two parallel, congruent polygonal bases connected by rectangular or parallelogram-shaped lateral faces. The bases can be any polygon, and the number of lateral faces equals the number of sides of the base.
Types of Prisms
Triangular Prism
Bases: Two congruent triangles
Lateral Faces: 3 rectangular faces
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Rectangular Prism (Cuboid)
Bases: Two congruent rectangles
Lateral Faces: 4 rectangular faces
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Hexagonal Prism
Bases: Two congruent hexagons
Lateral Faces: 6 rectangular faces
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Example
A rectangular prism, like a cereal box, has two rectangular bases and four rectangular lateral faces. If the base is 10 cm by 5 cm and the height is 20 cm, the volume is: Volume = Base Area × Height = (10 × 5) × 20 = 1000 cm³.
Volume Calculator
Calculate Volume
Choose whether to calculate the volume for a pyramid or prism. Enter the area of the base in square centimeters. Enter the height of the shape in centimeters.Result:
Key Concepts
Base
The flat polygon(s) that define the shape of a pyramid (one base) or prism (two bases). Example: A square base in a square pyramid.
Apex
The single vertex where the triangular faces of a pyramid meet. Example: The top point of the Great Pyramid of Giza.
Lateral Faces
The side faces connecting the base(s). In pyramids, they are triangles; in prisms, they are rectangles or parallelograms.
Volume Formulas
Pyramid: (1/3) × Base Area × Height
Prism: Base Area × Height
