331841_FES.qxd
12/6/04
11:21 AM
Page 4
FORMULAS FROM GEOMETRY
Triangle
Sector of Circular Ring
h a sin 1
Area bh
2
(Law of Cosines)
c2 a 2 b2 2ab cos c
p average radius,
w width of ring,
in radians
Area pw
a
h
θ
b
Right Triangle
s
h
4
b2
2
h
A
s
Parallelogram
Right Circular Cone
r 2h
3
Lateral Surface Area rr2 h2
h
h
h
Circle
r
rR h
3
Lateral Surface Area sR r
Volume b
b
r2
R2
s
h
Right Circular Cylinder
Area r 2
Volume r 2h
r
Circumference 2 r
Lateral Surface Area 2 rh
Sector of Circle
Sphere
R
r
h
4
Volume r 3
3
Surface Area 4 r 2
s
θ
r
Circular Ring
p average radius,
w width of ring
Area R 2 r 2
2 pw
r
Frustum of Right Circular Cone
a
a
in radians
r2
Area 2
s r
h
Volume b
h
Area a b
2
2
A area of base
Ah
Volume 3
s
3s2
Trapezoid
a
a
Cone
3s
Area bh
b
Circumference 2
Equilateral Triangle
Area w
Area ab
a
b
2
θ
Ellipse
c
(Pythagorean Theorem)
c2 a 2 b2
h
p
r
Wedge
r
p
R
w
A area of upper face,
B area of base
A B sec A
θ
B