CHAPTER 12AREAS AND

VOLUMES OF SOLIDS

12-1

PRISMS

PRISMPrisms are 3-dimensional solids that have

the following characteristics:

1. Bases

2. An altitude

3. Lateral faces

4. Lateral edges

BASES OF A PRISMEvery prism has two bases that are

congruent polygons lying on parallel planes.

**Bases of a prism can be any figure from chapter 11 except for circles:

Squares, rectangles, parallelograms, triangles, rhombuses, trapezoids, and regular polygons.

ALTITUDE OF A PRISM

An altitude of a prism is a segment that joins the two base planes and is perpendicular to both.

• The length of the altitude of a prism is also known as the height of the prism (H).

LATERAL FACESA prism has multiple “faces” which include the

bases of the prism.

The lateral faces of a prism that are not its bases are called lateral faces.

The lateral faces of an oblique prism are parallelogram. The lateral faces of a right prism are rectangles.

LATERAL EDGES

Lateral edges of a prism occur where adjacent lateral faces meet. How you

doin?What’s

up?

OBLIQUE VS. RIGHT PRISMOBLIQUE PRISM RIGHT PRISM

PRISMSRight Pentagonal Prism

BASES

LATERAL FACE

LATERAL EDGE

ALTITUDE (H)

PRISMS

Right Triangular Prism

BASE

LATERAL FACE

LATERAL EDGE

ALTITUDE (H)

BASE

PRISMS

Right Trapezoidal Prism

BASE

LATERAL FACE

LATERAL EDGE

ALTITUDE (H)

BASE

THEOREM 12-1

THEOREM 12-1

The lateral area of a right prism equals the perimeter of a base times the height of the prism.

L.A. = p • H

LATERAL AREAIn short, the lateral area of a right prism is

the sum of the areas of the lateral faces.

Remember, the lateral faces of a right prism are rectangles.

Lateral AREA is measured in square units (units²).

TOTAL AREATotal area of a prism refers to the sum of the

areas of all faces and, just like lateral area, is measured in square units.

“All faces” of a prism include the lateral faces and bases.

Total area of a prism is found by adding the lateral area to the area of both of the bases.

T.A. = L.A. + 2B

THEOREM 12-2

THEOREM 12-2

The volume of a right prism equals the area of a base times the height of the prism.

V = B • H

VOLUME

Volume is a 3-dimensional measure and is reported in cubic units (units³).

The formula for volume includes a capital B which represents the area of the base.

AREA OF A BASE OF A PRISM

“B” can be any of the following:

1. s² Square

2. bh Rectangle, parallelogram

3. ½ bh Triangle

4. ½ d1d2 Rhombus

5. ½ h (b1 + b2) Trapezoid

6. ½ ap Regular polygon

CLASSWORK/HOMEWORK12.1 ASSIGNMENT

Classwork:• Pg. 477, Classroom Exercises 2-10 even

Homework:• Pgs. 478-479, Written Exercises 2-26 even