chapter 12 areas and volumes of solids 12-1 prisms
TRANSCRIPT
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