CHAPTER 12 AREAS AND VOLUMES OF SOLIDS 12-1 PRISMS.
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Transcript of CHAPTER 12 AREAS AND VOLUMES OF SOLIDS 12-1 PRISMS.
![Page 1: CHAPTER 12 AREAS AND VOLUMES OF SOLIDS 12-1 PRISMS.](https://reader036.fdocuments.us/reader036/viewer/2022080223/56649ee65503460f94bf6bc5/html5/thumbnails/1.jpg)
CHAPTER 12AREAS AND
VOLUMES OF SOLIDS
12-1
PRISMS
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PRISMPrisms are 3-dimensional solids that have
the following characteristics:
1. Bases
2. An altitude
3. Lateral faces
4. Lateral edges
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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.
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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).
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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.
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LATERAL EDGES
Lateral edges of a prism occur where adjacent lateral faces meet. How you
doin?What’s
up?
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OBLIQUE VS. RIGHT PRISMOBLIQUE PRISM RIGHT PRISM
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PRISMSRight Pentagonal Prism
BASES
LATERAL FACE
LATERAL EDGE
ALTITUDE (H)
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PRISMS
Right Triangular Prism
BASE
LATERAL FACE
LATERAL EDGE
ALTITUDE (H)
BASE
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PRISMS
Right Trapezoidal Prism
BASE
LATERAL FACE
LATERAL EDGE
ALTITUDE (H)
BASE
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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
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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).
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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
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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
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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.
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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
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CLASSWORK/HOMEWORK12.1 ASSIGNMENT
Classwork:• Pg. 477, Classroom Exercises 2-10 even
Homework:• Pgs. 478-479, Written Exercises 2-26 even