Surface Area
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 ,
// 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 – Edges
are Altitudes.
Oblique Prism
Lateral Area – The sum of the areas of the
lateral faces (sides)
• Right Prisms - Lateral Faces are Rectangles
A = l•w
Base Area – The sum of the areas
of the 2 bases
• Rectangle: A = l•w
• Triangle: A = ½bh
• Polygon: A = ½bh
Total Surface Area = Lateral Area + Base Area
Ex.1: Use the net to find the Surface Area of the rectangular Prism.
Area of Bases: A = l•w
2 different Lats: A = l•w
4
5cm
3cm
3
4
3
15
20
15
12
3
20
5
4cm
SA = LA + Area of Bases
= 70cm2 + 24cm2
= 94cm2
12
3
Ex.2: Find the total surface area of the
following triangular prism.
5cm
LA = l•w (Area of Sides)
(5 x 12) = 60cm2
5cm
(5 x 12) = 60cm2
12cm
(6 x 12) = 72cm2
6cm
192cm2
Area of Triangle
BA = ½bh
= ½(6)(4)
= 12cm2
x2
24cm2
5
a2 + b2 = c2
h2
+
32 =
h=4
52
SA = LA + BA
h
= 192cm2 + 24cm2
6
3
= 216cm2
Ex.2: Find the total surface area of the
following regular hexagonal prism.
LA = l•w
(10 x 12) = 120m2
12m
x 6
720m2
BA = ½ap
= ½(8.7)(60)
= 260m2
x2
520m2
10
30°
a
10m
SA = LA + BA
5
Tan 30 = 5/a
= 720m2 + 520m2
.577 = 5/a
= 1240m2
a = 8.7
II. Finding Surface Area of a Cylinder
 Cylinder
 Has 2 , // bases
 Base → Circle
r
 C = 2πr
 A = πr2
height
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.4: 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
What did I learn today??
 Find the area of the lateral sides first!!
 Usually rectangles
 Be careful, the rectangles are not always the
same size.
 Second, find the area of the Base
 Rectangle, Triangle, Polygon, or a Circle
 There are always 2 bases in prisms.
 Multiply by 2!