section 12-1 prisms. prism a 3-dimensional figure with two congruent, parallel faces the congruent,...

Section 12-1Prisms

Prism• a 3-dimensional figure with

two congruent, parallel faces•The congruent, parallel faces are called the bases.•The bases lie in parallel planes.

Base

Base

Altitude of a prism• a segment joining the two

base planes; it is perpendicular to both planes

• The length of the altitude is the height of the prism!

altitude

• the faces that are not its bases•In the shape of parallelograms

Lateral faces of a prism

• the parallel segments where adjacent lateral faces intersect

Lateral Edges

Types of prisms1. Right Prism:

– have rectangles for the lateral faces

– Lateral edges are altitudes

2. Oblique prism: – Lateral edges are NOT altitudes

Example of a Right Prism:

Example of an Oblique Prism:

Height

A prism is named by the shape of its

base.

Some Examples of Right Prisms:

Rectangular Prism:

Base

Base

If the edges have equal length then the rectangular

prism is called a cube.

Triangular Prism:

: Pentagonal Prism

Base

Base

Base

Base

Hexagonal Prism:

And the list goes on…..

Base

Base

Lateral area•The sum of the areas of the lateral faces

Theorem 12-1• The lateral area of a right

prism equals the perimeter of a base times the height of the prism.

L.A. = Ph

Total Area• The sum of the areas of all its

faces

T.A. = L.A. + B2

Total AreaLateral Area # of Bases

Area of a Base

volume• The number of cubic units enclosed by a three dimensional object.

Therefore volume is measured in cubic units.

Theorem 12-2• The volume of a right prism equals the area of a base times the height of the prism.

BhV