2. Ch5.5_5.6_ 3DFiguresAreas.notebook November 22, 2011
Polygon: two dimensional shape
Polyhedron: three dimensional figure
Face: flat surface on the figure
6 faces
Vertex: corner of the figure
8 vertices
Edge: where 2 faces meet
a 12 edges
ul
o rm
's F
r
Eul
e F + V E = 2
6 + 8 12 = 2
How many faces, vertices, and edges
does each 3D figure have?
Trangular Prism
F + V E = 2
Pentagonal Pyramid
F + V E = 2
3. Ch5.5_5.6_ 3DFiguresAreas.notebook November 22, 2011
SURFACE AREA FORMULAS
To find the SA of a solid, add up the areas of each face
=
l = length
Rectangular Prism w = width
h = height
Opposite faces are congruent
4 2 lw + 2 lh + 2 wh
or
6 1 2 (lw + lh + wh)
Regular Triangular Prism
2 congruent Δ bases
3 congruent lateral faces
3 3
2
5
3
Regular Pyramid 1 base
congruent Δ faces
1
6
B +( 2 bh) n
B = area of base
b = base of Δ
5 5 h = height of Δ
n = # of Δ's
Cylinder 2 circular bases
1 lateral surface
2πr2 + 2πrh
8 Area of bases + circumference x height
2
Cone 1 circular base
1 lateral surface
7 πr2 + πrs
s = slant height
3
Sphere
4πr2
5
12
6
