1. 9.1
Prisms, Area, & Volume
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2. Prisms A polygon is “flat” since all its sides lie in the same plane.
The figure that is the counterpart of a polygon in space is called a polyhedron.
A prism is a special type of polyhedron.
The sides of a prism are called faces.
2 of the faces, called bases, are congruent polygons lying in parallel planes. The prism is named by its bases.
The faces that are not bases, called lateral faces, are parallelograms.
A prism in which the lateral edges are perpendicular to the base edges at their point of intersection(if the lateral faces are rectangles) the prism is a right prism, otherwise, it is called an oblique prism.
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4. Area of Prism Lateral area: sum of the areas of all lateral faces.
Theorem 9.1.1: Lateral area of a Right prism, where P is the perimeter of a base, h is the height of the prism
L = hP
Theorem 9.12: The Total Surface Area T of any prism with lateral area L and base area B is given by twice the Base area plus the Lateral area:
T = 2B + L
Ex. 2,3 p. 406
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5. Regular Prism Volume of a Prism
A regular prism is a right prism whose base is a regular polygon.
A cube is a right square prism whose edges are congruent.
Ex. 4 p. 407, 5 p. 408
Volume of a Prism
Postulate 24: (Volume Postulate) Corresponding to every solid is a unique positive number V known as the volume of that solid.
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6. Volume of a right rectangular prism
Postulate 25: The volume of a right rectangular prism is given by
V = l w h
where l measures the length, w the width, and h is the altitude of the prism.
Ex. 6 p. 409
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7. Volume of a Prism Postulate 26: The volume, V, of any prism is V = Bh
Volume of a rectangular solid:
V = Bh = (l x w)h
Examples 7 and 8 p. 410
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