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

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Section 12-1 Prisms

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Page 1: Section 12-1 Prisms. Prism a 3-dimensional figure with two congruent, parallel faces The congruent, parallel faces are called the bases. The bases lie

Section 12-1Prisms

Page 2: Section 12-1 Prisms. Prism a 3-dimensional figure with two congruent, parallel faces The congruent, parallel faces are called the bases. The bases lie

Prism• a 3-dimensional figure with

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

Page 3: Section 12-1 Prisms. Prism a 3-dimensional figure with two congruent, parallel faces The congruent, parallel faces are called the bases. The bases lie

Base

Base

Page 4: Section 12-1 Prisms. Prism a 3-dimensional figure with two congruent, parallel faces The congruent, parallel faces are called the bases. The bases lie

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!

Page 5: Section 12-1 Prisms. Prism a 3-dimensional figure with two congruent, parallel faces The congruent, parallel faces are called the bases. The bases lie

altitude

Page 6: Section 12-1 Prisms. Prism a 3-dimensional figure with two congruent, parallel faces The congruent, parallel faces are called the bases. The bases lie

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

Lateral faces of a prism

Page 7: Section 12-1 Prisms. Prism a 3-dimensional figure with two congruent, parallel faces The congruent, parallel faces are called the bases. The bases lie

• the parallel segments where adjacent lateral faces intersect

Lateral Edges

Page 8: Section 12-1 Prisms. Prism a 3-dimensional figure with two congruent, parallel faces The congruent, parallel faces are called the bases. The bases lie

Types of prisms1. Right Prism:

– have rectangles for the lateral faces

– Lateral edges are altitudes

2. Oblique prism: – Lateral edges are NOT altitudes

Page 9: Section 12-1 Prisms. Prism a 3-dimensional figure with two congruent, parallel faces The congruent, parallel faces are called the bases. The bases lie

Example of a Right Prism:

Example of an Oblique Prism:

Height

Page 10: Section 12-1 Prisms. Prism a 3-dimensional figure with two congruent, parallel faces The congruent, parallel faces are called the bases. The bases lie

A prism is named by the shape of its

base.

Page 11: Section 12-1 Prisms. Prism a 3-dimensional figure with two congruent, parallel faces The congruent, parallel faces are called the bases. The bases lie

Some Examples of Right Prisms:

Rectangular Prism:

Base

Base

Page 12: Section 12-1 Prisms. Prism a 3-dimensional figure with two congruent, parallel faces The congruent, parallel faces are called the bases. The bases lie

If the edges have equal length then the rectangular

prism is called a cube.

Page 13: Section 12-1 Prisms. Prism a 3-dimensional figure with two congruent, parallel faces The congruent, parallel faces are called the bases. The bases lie

Triangular Prism:

: Pentagonal Prism

Base

Base

Base

Base

Page 14: Section 12-1 Prisms. Prism a 3-dimensional figure with two congruent, parallel faces The congruent, parallel faces are called the bases. The bases lie

Hexagonal Prism:

And the list goes on…..

Base

Base

Page 15: Section 12-1 Prisms. Prism a 3-dimensional figure with two congruent, parallel faces The congruent, parallel faces are called the bases. The bases lie

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

Page 16: Section 12-1 Prisms. Prism a 3-dimensional figure with two congruent, parallel faces The congruent, parallel faces are called the bases. The bases lie

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

Page 17: Section 12-1 Prisms. Prism a 3-dimensional figure with two congruent, parallel faces The congruent, parallel faces are called the bases. The bases lie

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

Page 18: Section 12-1 Prisms. Prism a 3-dimensional figure with two congruent, parallel faces The congruent, parallel faces are called the bases. The bases lie

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

Therefore volume is measured in cubic units.

Page 19: Section 12-1 Prisms. Prism a 3-dimensional figure with two congruent, parallel faces The congruent, parallel faces are called the bases. The bases lie

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

BhV