Sect. 1.7
G.GMD.3 / Math Pract. 2,6
Sect. 1.7 ­ Three­Dimensional Figures
Polyhedron ­ a solid enclosing a single
region of space that is made up of
only flat surfaces. Face ­ each flat surface that is a
polygon.
Edges ­ The lines where the faces
intersect. Face
Edge
Vertex
Mr. VanKeuren / G.H.S. / Oct., 2014
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Sect. 1.7
G.GMD.3 / Math Pract. 2,6
Types of Solids:
Polyhedrons
Prism ­ a polyhedron with two
parallel congruent faces called
bases connected by Bases
parallelograms.
Vertex
Pyramid ­ a polyhedron that has a
polygonal base and three or
more triangular faces that meet
at a common vertex.
Base
Bases
Not Polyhedrons
Cylinder ­ a solid with congruent
parallel circular bases connected
by a curved surface
Vertex
Cone ­ a solid with a circular base
connected by a curved surface
to a single vertex.
Base
Sphere ­ is set of points in space
that are the same distance from
a given point. There are no faces, edges, or vertices.
Mr. VanKeuren / G.H.S. / Oct., 2014
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Sect. 1.7
G.GMD.3 / Math Pract. 2,6
Polyhedrons (or Polyhedra) are named by
the shape of their bases. (They can be either prisms or pyramids.)
Triangular Prism
Square
Pyramid
Regular Polyhedron ­ when all of its faces
are regular congruent polygons and all
of its edges are congruent. There are
exactly five types of regular polyhedrons
called Platonic Solids. (Plato 427­347 B.C.)
Mr. VanKeuren / G.H.S. / Oct., 2014
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Sect. 1.7
G.GMD.3 / Math Pract. 2,6
Surface Area ­ a two­dimensional measurement
of the surface of a solid figure. (The sum of
the areas of each of its faces, in square units.)
Volume ­ the measure of the amount of space enclosed by a solid figure. (The cubic unit
amount of what it takes to fill the interior space.)
Mr. VanKeuren / G.H.S. / Oct., 2014
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Sect. 1.7
G.GMD.3 / Math Pract. 2,6
Formulas:
Prism
S.A. = (Perimeter of base)x(Height) + 2(Area of Base)
S = Ph + 2B
V = (Area of Base)x(Height)
V = Bh
Regular Pyramid
S.A. = (1/2)(Perimeter of base)(Slant height) +
(Area of base)
S = (1/2)P + B
V = (1/3)(Area of base)x(Height)
V= (1/3)Bh
Cylinder
S.A. = 2 (Radius)x(Height) + 2 (Radius)2
S = 2 rh + 2 r2
V = (Radius)2x(Height)
V = r2h
Cone
S.A. = (Radius)x(Slant Height) + (Radius)2
S = r + r2
V = (1/3) (Radius)2x(Height)
V = (1/3) r2h
Mr. VanKeuren / G.H.S. / Oct., 2014
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Sect. 1.7
G.GMD.3 / Math Pract. 2,6
Formulas : (last one)
Sphere
S.A. = 4 r2
V = (4/3) r3
Mr. VanKeuren / G.H.S. / Oct., 2014
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