Download Prisms Area of a Prism

Math 53 "Winter ’09"
8.1 "Prisms, Area, and Volume"
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Objectives:
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Finding the area and volume of prisms
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Prisms
If two congruent polygons lie in parallel planes in such a way that their corresponding sides are parallel
and if the corresponding vertices of these polygons are joined by line segments, then the "solid" that results is a prism.
De…nition:
"Right Prism"
A right prism is a prism in which the lateral edges are perpendicular
to the base edges at their points of intersection.
De…nition:
"Oblique Prism"
An oblique prism is a prism in which the parallel lateral edges are
oblique to the base edges at their points of intersection.
Area of a Prism
De…nition:
"Lateral Area"
kThe lateral area L of a prism is the sum of the areas of all lateral facesk
Theorem 8.1.1:
The lateral area L of any prism whose altitude has measure h and
whose base has perimeter P is given by:
Page: 1
Bibiana Lopez
Elementary Geometry by Alexander and Koeberlein
8.1
Example 1: (Finding the lateral area)
The bases of the right prism shown are equilateral pentagons with sides of length 3 in. each.
If the altitude of the prism is 4 in., …nd the lateral area of the prism.
De…nition:
"Total Area"
kFor any prism, the total area T is the sum of the lateral area and the areas of the basesk
Theorem 8.1.2:
The total area T of any prism with lateral area L and base area B is given by
Example 2: (Finding the total area)
For a right triangular prism, suppose that the sides of the triangular base measure 3 f t; 4 f t; and 5 f t.
The altitude is 6 f t: Find the total area.
De…nition:
"Regular Prism"
kA regular prism is a right prims whose bases are regular polygonsk
Example 3: (Finding the total area)
Find the total area of the regular hexagonal prism with sides of length 4 in: and altitude 10 in:
Page: 2
Bibiana Lopez
Elementary Geometry by Alexander and Koeberlein
De…nition:
8.1
"Cube"
kA cube is a right square prims whose edges are congruentk
Example 4:
The total area of the right square prism is 210 cm2 .
Find the length of a side of the square base if the altitude of the prism is 8 cm:
Volume of a Prism
Postulate 24:
Volume Postulate
kCorresponding to every solid is a unique positive number V known as the volume of that solidk
Postulate 25:
The volume of a right rectangular prism is given by
where l measures the length, w is the width, and h is the altitude of the prism.
Example 5: (Finding the volume)
Find the volume of a box whose dimensions are 2 f t; 16 in; and
20 in:
Postulate 26:
The volume of a right prism is given by
where B is the area of a base and h is the altitude of the prism.
Page: 3
Bibiana Lopez
Elementary Geometry by Alexander and Koeberlein
8.1
Example 6: (Finding the volume)
For a right triangular prism, suppose that the sides of the triangular base measure 3 f t; 4 f t; and 5 f t,
the altitude is 6 f t: Find the volume.
Example 7:
A concrete pad 4 in. thick is to have a length of 36 ft. and a width of 30 ft.
How many cubic yards of concrete must be poured? [Hint: 1 yd3 = 27 f t3 ]
Page: 4
Bibiana Lopez