1. Surface Area of Prisms & Cylinders
Objectives:
1) To find the surface area of a prism.
2) To find the surface area of a cylinder.

2. 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)

3. Right Prisms vs Oblique Prisms
Right Prism – Edges are Altitudes.

4. 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

5. 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 12 3 3 4 3 5 15 20 15 20
3cm
4cm
SA = LA + Area of Bases
= 70cm2 + 24cm2
= 94cm2 3 12

6. Ex.2: Find the total surface area of the following triangular prism.
5cm
LA = l•w (Area of Sides)
(5 x 12) = 60cm2
(6 x 12) = 72cm2
5cm
12cm
6cm
Area of Triangle
192cm2
BA = ½bh
= ½(6)(4)
= 12cm2
x 2
24cm2 5 3 h
SA = LA + BA
= 192cm2 + 24cm2
= 216cm2
a2 + b2 = c2
h = 52
h = 4 6

7. Ex.2: Find the total surface area of the following regular hexagonal prism.
LA = l•w
(10 x 12) = 120m2
x 6
12m
720m2 10
BA = ½ap
= ½(8.7)(60)
= 260m2
x 2
520m2
10m
30° a
SA = LA + BA
= 720m m2
= 1240m2 5
Tan 30 = 5/a
.577 = 5/a
a = 8.7

8. II. Finding Surface Area of a Cylinder
Has 2 , // bases
Base → Circle
C = 2πr
A = πr2 r
height r h r

9. Net of a Cylinder: LA is just a Rectangle! LA = 2rh BA = r2
Area of a circle
LA = 2rh
BA = r2 r
Circumference of the circle
SA = LA + 2BA

10. Ex.4: SA of a right cylinder
LA = 2rh
= 2(6)(9)
= 108ft2
= 339.3ft2
6ft
Area of Base
BA = r2
= (6)2
= 36ft2
9ft
x 2
SA = LA + BA
= 339.3ft ft2
= 565.5ft2
= 72ft2
= ft2

11. 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!