10-6 Solid Figures
Learn to name solid figures.
Course 1
10-6 Solid
InsertFigures
Lesson Title Here
Vocabulary
polyhedron
face
edge
vertex
prism
base
pyramid
cylinder
cone
Course 1
10-6 Solid Figures
A polyhedron is a three-dimensional
object, or solid figure, with flat surfaces,
called faces, that are polygons.
When two faces of a solid figure share a
side, they form an edge. On a solid
figure, a point at which three or more
edges meet is a vertex (plural: vertices).
Course 1
10-6 Solid Figures
Try This: Example 1
Identify the number of faces, edges, and
vertices on each solid figure.
6 faces
A.
12 edges
8 vertices
B.
5 faces
9 edges
6 vertices
Course 1
10-6 Solid Figures
A prism is a polyhedron with two congruent,
parallel bases, and other faces that are all
parallelograms. A prism is named for the shape
of its bases.
Course 1
10-6 Solid Figures
A cylinder also has two congruent, parallel
bases, but bases of a cylinder are circular.
Cylinders are not polyhedra because not every
surface is a polygon.
Course 1
10-6 Solid Figures
A pyramid has one polygon shaped base, and the
other faces are triangles that come to a point. A
pyramid is named for the shape of its base.
Course 1
10-6 Solid Figures
A cone has a circular base and a curved
surface that comes to a point. Cones are not
polyhedra because not every surface is a
polygon.
Helpful Hint
The point of a cone is called its vertex.
Course 1
10-6 Solid Figures
Additional Example 2A: Naming Solid Figures
Name the solid figures represented by the
object.
There is a curved surface.
A.
The figure is not a polyhedron.
There are two congruent, parallel
bases.
The bases are circles.
The figure represents a cylinder.
Course 1
10-6 Solid Figures
Additional Example 2B: Naming Solid Figures
Name the solid figures represented by the
object.
B.
All the faces are flat and are
polygons.
The figure is a polyhedron.
There is one base and the other
faces are triangles that meet at a
point, so the figure is a pyramid.
The base is a triangle.
The figure is a triangular pyramid.
Course 1
10-6 Solid Figures
Additional Example 2C: Naming Solid Figures
Name the solid figures represented by the
object.
C.
All the faces are flat and are
polygons.
The figure is a polyhedron.
There are two congruent, parallel
bases, so the figure is a prism. The
bases are rectangles.
The figure is a rectangular prism.
Course 1
10-6 Solid Figures
Try This: Example 2A
Name the solid figures represented by the
object.
A.
All the faces are flat and are
polygons.
The figure is a polyhedron.
There is one base and the other
faces are triangles that meet at a
point, so the figure is a pyramid.
The base is a square.
The figure is a square pyramid.
Course 1
10-6 Solid Figures
Try This: Example 2B
Name the solid figures represented by the
object.
B.
All the faces are flat and are
polygons.
The figure is a polyhedron.
There are two congruent, parallel
bases, so the figure is a prism. The
bases are rectangles.
The figure is a rectangular prism.
Course 1
10-6 Solid Figures
Try This: Example 2C
Name the solid figures represented by the
object.
There is a curved surface.
C.
The figure is not a polyhedron.
There are two congruent, parallel
bases.
The bases are circles.
The figure represents a cylinder.
Course 1
10-7 Surface Area
Learn to find the surface areas of prisms,
pyramids, and cylinders.
Course 1
10-7 Surface
Insert Lesson
Area Title Here
Vocabulary
surface area
net
Course 1
10-7 Surface Area
The surface area of a solid figure is
the sum of the areas of its surfaces. To
help you see all the surfaces of a solid
figure, you can use a net. A net is the
pattern made when the surface of a
solid figure is laid out flat showing
each face of the figure.
Course 1
10-7 Surface Area
Additional Example 1A: Finding the Surface
Area of a Prism
Find the surface area S of the prism.
A. Method 1: Use a net.
Draw a net to help you see each face of the prism.
Use the formula A = lw to find the area of each face.
Course 1
10-7 Surface Area
Additional Example 1A Continued
A: A = 5  2 = 10
B: A = 12  5 = 60
C: A = 12  2 = 24
D: A = 12  5 = 60
E: A = 12  2 = 24
F: A = 5  2 = 10
Add the areas of each face.
S = 10 + 60 + 24 + 60 + 24 + 10 = 188
The surface area is 188 in2.
Course 1
10-7 Surface Area
Additional Example 1B: Finding the Surface Area
of a Prism
Find the surface area S of each prism.
B. Method 2: Use a three-dimensional drawing.
Find the area of the front, top, and side, and
multiply each by 2 to include the opposite faces.
Course 1
10-7 Surface Area
Additional Example 1B Continued
Front: 9  7 = 63
63  2 = 126
Top:
9  5 = 45
45  2 = 90
Side:
7  5 = 35
35  2 = 70
S = 126 + 90 + 70 = 286 Add the areas of each face.
The surface area is 286 cm2.
Course 1
10-7 Surface Area
Try This: Example 1A
Find the surface area S of the prism.
A. Method 1: Use a net.
3 in.
6 in.
11 in.
11 in.
3 in.
A
6 in. 3 6 in. 3
in.
in.
B
C
D
F
E
3 in.
Draw a net to help you see each face of the prism.
Use the formula A = lw to find the area of each face.
Course 1
10-7 Surface Area
Try This: Example 1A
A: A = 6  3 = 18
B: A = 11  6 = 66
C: A = 11  3 = 33
D: A = 11  6 = 66
11 in.
E: A = 11  3 = 33
3 in.
A
6 in. 3 6 in. 3
in.
in.
B
C
D
F
F: A = 6  3 = 18
Add the areas of each face.
S = 18 + 66 + 33 + 66 + 33 + 18 = 234
The surface area is 234 in2.
Course 1
E
3 in.
10-7 Surface Area
Try This: Example 1B
Find the surface area S of each prism.
B. Method 2: Use a three-dimensional drawing.
top
front
8 cm
6 cm
side
10 cm
Find the area of the front, top, and side, and
multiply each by 2 to include the opposite faces.
Course 1
10-7 Surface Area
Try This: Example 1B Continued
top
front
8 cm
6 cm
Front: 10  8 = 80
Top:
Side:
10  6 = 60
8  6 = 48
side
10 cm
80  2 = 160
60  2 = 120
48  2 = 96
S = 160 + 120 + 96 = 376 Add the areas of each face.
The surface area is 376 cm2.
Course 1
10-7 Surface Area
The surface area of a pyramid equals
the sum of the area of the base and the
areas of the triangular faces. To find the
surface area of a pyramid, think of its
net.
Course 1
10-7 Surface Area
Additional Example 2: Finding the Surface Area
of a Pyramid
Find the surface area S of the pyramid.
S = area of square + 4  (area of
triangular face)
1
S = s2 + 4  (__bh)
2
1
S = 72 + 4  ( __ 7  8) Substitute.
2
S = 49 + 4  28
S = 49 + 112
S = 161
The surface area is 161 ft2.
Course 1
10-7 Surface Area
Try This: Example 2
Find the surface area S of the pyramid.
5 ft
5 ft
5 ft
Course 1
S = area of square + 4  (area of
triangular face)
10 ft
1
S = s2 + 4  (__bh)
2
1
S = 52 + 4  ( __ 5  10) Substitute.
2
10 ft
S = 25 + 4  25
S = 25 + 100
S = 125
The surface area is 125 ft2.
10-7 Surface
Insert Lesson
Area Title Here
Lesson Quiz
Find the surface area of each figure. Use
3.14 for .
1. rectangular prism with base length 6 ft, width
5 ft, and height 7 ft 214 ft2
2. cylinder with radius 3 ft and height 7 ft 188.4 ft2
3. Find the surface area of the figure shown.
208 ft2
Course 1