Unit 4: Exploring Solids (12.1­12.2) p.719­734
PYRAMID
PRISM
CYLINDER CONE
SPHERE
1
Face:
A polygon that makes up a side of the solid figure
Edge:
A segment that is formed by the intersection of 2 faces
Face
Base
Edge
Vertex: A point where 3 or more edges meet
Vertex
Bases:
Are the 2 congruent and parallel faces of a prism
Lateral Faces: Are the faces of the figure that are NOT the bases
Polyhedron: solid that is bounded by polygons
polyhedra/polyhedrons (plural)
2
Regular Polyhedron: All faces are congruent
Convex Polyhedron: any two points on a face or edge must be on or inside the shape if connected by a segment
Ex: Ex: Concave Polyhedron: a segment can be drawn outside the shape given two points on a face or edge
Cross Section: intersection of a plane and a solid 3
Platonic Solids: 5 regular polyhedra
Tetrahedron: 4 faces (triangles)
Cube: 6 faces (squares)
Octahedron: 8 faces (triangles)
Dodecahedron: 12 faces (pentagons)
Icosahedron: 20 faces (triangles)
Euler's Theorem: The number of faces (F), vertices, (V), and edges (E) of a polyhedron are related by:
F + V = E + 2 4
Ex: Is the solid a polyhedron?
a)
c)
b)
d)
5
Ex: How many faces, edges, and vertices? a)
b)
Are the polyhedrons regular? Why/why not? 6
Ex: Use Euler's Theorem to find the number of vertices in the given polyhedron with the given faces.
b) 14 faces
8 hexagons
6 squares
a) 20 faces
all triangles
c) 8 faces
4 hexagons
4 triangles
7
HW: p.723­725
#10­38 even
#42­52 even
8
NETS OF SOLID FIGURES
9
NETS OF SOLID FIGURES
10
Surface Area of Prisms and Cylinders
Surface Area (SA):
The area of all of the faces added together
Lateral Area (LA):
The area of only the lateral faces added together
Height (h): Is the distance between to 2 bases of a prism or cylinder
FORMULAS
PRISM: LA = Ph
SA = 2B + Ph
CYLINDER:
P: Perimeter of the base
B: Area of the base
h: Height of the Prism
LA = 2πrh
SA = LA + 2πr2
r:
h:
radius of circle
height of cylinder
11
Example 1:
Find the surface area and the lateral area for each solid figure.
a)
b)
9 m
24 in
28 m
12 m
8 in
12 in
c)
d)
4 cm
The area of one base of a right regular hexagonal prism is 54 square inches. The apothem of the hexagon is 3 inches. The height of the prism is 7 inches. What is the LA and SA?
6 cm
7 cm
12
Example 2:
Find the surface area and lateral area given the solid.
a)
b)
8 cm
32 in
14 cm
13 in
c)
d)
Find the SA and LA of a right cylinder with a height of 3 yards and a diameter of 7 yards.
21 m
5 m
13
Ex: Given the surface area, find the missing length. SA = 870 m2
12 m
x
13 m
14
Ex: What is the surface area of the object below? 12 ft
12 ft
8 ft
15
HW: p.732­733
#14­40 even
#42­44
16