Surface Area and
Volume of Prisms
& Cylinders
Objectives:
1) To find the surface area of a prism.
2) To find the surface area of a cylinder.
I. Surface Area of a Prism
 Prism – Is a polyhedron with exactly 2
congruent, parallel faces, called bases.
 Name it by the shape of its bases.
Bases are Rectangles:
Lateral Faces – All faces that
are not bases. (Sides)
Right Prisms vs Oblique
Prisms
Right Prism – Lateral
faces are rectangles.
Oblique Prism –
Lateral faces are
parallelograms
Total Surface Area = Lateral Area + 2 Base Area
Lateral Area – • If the base is a
regular polygon all 4
rectangles will be
congruent
•If the base is a non
regular polygon you
should look at
individual rectangles
and calculate their
areas with A = l•w
Total Surface Area = Lateral Area + 2 Base Area
Base Area – • Rectangle: A = l•w
• Triangle: A = ½bh
Ex.1: Find the Surface Area of the rectangular Prism.
Area of Bases:
Lateral Area
A = l•w
Left and right rectangles
are congruent
= 4•3 = 12 cm2
5cm
A = l•w= 3•5 = 15 cm2
Front and back
rectangles are congruent
3cm
A = l•w= 4•5 = 20 cm2
Total = 15+15+20+20
4cm
SA = LA + BA
= 70cm2 + 24cm2
= 94cm2
=70 cm2
Ex.2: Find the total surface area of the
following triangular prism.
5cm
LA = l•w
(5 x 12) = 60cm2
5cm
(5 x 12) = 60cm2
(6 x 12) = 72cm2
h
4 cm
6cm
192cm2
BA = ½bh
= ½(6)(4)
= 12cm2
x2
24cm2
SA = LA + BA
= 192cm2 + 24cm2
= 216cm2
12cm
II. Finding Surface Area of a Cylinder
 Cylinder
r
 Has 2 congruent, parallel
bases
 Base → Circle
height
 C = 2πr
 A = πr2
r
h
r
Net of a
Cylinder:
LA is just a Rectangle!
LA = 2rh
Area of a circle
BA = r2
r
Circumference of the circle
SA = LA + 2BA
Ex.3: SA of a right cylinder
LA = 2rh
6ft
9ft
= 2(6)(9)
Area of Base
= 108ft2
BA = r2
= 339.3ft2
= (6)2
= 36ft2
x2
SA = LA + BA
= 72ft2
= 339.3ft2 + 226.2ft2
= 226.2 ft2
= 565.5ft2