Geometric Shape

Surface
Area
B = area of
the base
P = perimeter
of the base 
Volume
B = area of
the base
P = perimeter
of the base 
prism
(general)

B = area of base

P = perimeter of base

h = height

SA = 2B +
Ph 
V = Bh 
triangular
prism

a = altitude

b = base

h = #height

SA = 2B +
Ph
SA = 2(1/2ab) + (b + c + d)h
SA = ab + (b + c + d)h

V = Bh
V = 1/2 abh

rectangular
prism

l = length

w = width

h = height

SA = 2B + Ph
SA = 2(lw) + (2l + 2w)h

V = lwh

Regular
square prism

SA = 2B + Ph
SA = 2(s^{2}) + (4s)h

V = Bh
V = s^{2}h

regular
pentagonal prism

a = apothem length

s = side length

n = #sides
 h = height

SA = 2B + Ph
SA = 2(1/2ans) + nsh
SA = 2(1/2a)(5)s + 5sh
SA = 5as + 5sh

V = Bh
V = 1/2ansh
V = 1/2a(5)sh
V = 5/2ash

regular
hexagonal prism

a = apothem length

s = side length

n = #sides
 h = height

SA = 2B + Ph
SA = 2(1/2ans) + nsh
SA = 2(1/2a)(6)s + 6sh
SA =6as + 6sh

V = Bh
V = 1/2ansh
V = 1/2a(6)sh
V = 3ash

cube

SA = 2B + Ph
SA = 2(s^{2}) + (4s)s = 6s^{2}

V = Bh
V = s^{3}

regular
pyramid (general)

B = area of base

s = side length
 l = slant heigth

SA = B + n(1/2sl)
l = slant height 
V = 1/3Bh 
regular
triangular pyramid

a = apothem length

s = side length

n = #sides
 l = slant
height
 h = height

SA
= B + n(1/2sl)
SA = 1/2as + (3)(1/2sl)
SA = 1/2as + 3/2sl
l = slant height 
V
= 1/3Bh
V = 1/3(1/2 ab)h
V = 1/6 abh

regular
square pyramid

s = side length

n = #sides
 l = slant height
 h = height

SA
= B + n(1/2sl)
SA = s^{2} + (4)(1/2sl)
SA = s^{2} + 2sl
l = slant height 
V = 1/3Bh
V = 1/3(b^{2})h
= 1/3b^{2}h

regular
pentagonal pyramid

a = apothem length

s = side length

n = #sides
 l = slant height
 h = height

SA
= B + n(1/2sl)
SA = 1/2a(5)s + (5)(1/2sl)
SA = 5/2as + 5/2sl
l = slant height 
V = 1/3Bh
V = 1/3(1/2anb)h
V = 1/6 anbh

regular
hexagonal pyramid

a = apothem length

s = side length

n = #sides
 l = slant height
 h = height

SA
= B + n(1/2sl)
SA = 1/2a(6)s + (6)(1/2sl)
SA = 3as + 3sl
l = slant height 
V = 1/3Bh
V = 1/3(1/2anb)h
V = 1/6 anbh

cylinder

B = area of base

P = perimeter of base
 r = radius of circle

h = height

SA
= 2B + Ph
SA = 2(π r^{2})
+ (2πr)h

V
= Bh
V = π r^{2}h

cone

B = area of base
 r = radius of circle

h = height

SA
= πrs + πr^{2}
Explanation 
V
= 1/3 Bh
V = 1/3πr^{2}h
The volume of a cone is one third the volume
of the corresponding cylinder. 
sphere
r = radius of circle 
SA
= 4πr^{2}

V
= 4/3πr^{3}
