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.
Ms. Olifer

2. I. Surface Area of a Prism
Prism – Is a polyhedron w/ 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)
LA = Ph
Base Area – The sum of the areas of the 2 bases
Rectangle: A = l•w
Triangle: A = ½bh
Total Surface Area = Lateral Area + 2Base Area

5. Ex.1: Find the Surface Area of the rectangular Prism.
Area of Bases: A = l•w
5cm
3cm
4cm
SA = LA + BA
= 70cm2 + 24cm2
= 94cm2

6. Ex. 2: Find the total surface area of the following triangular prism
Ex.2: Find the total surface area of the following triangular prism. The base is an isosceles triangle.
5cm
5cm
12cm
LA = Ph
6cm
192cm2
BA = ½bh
= ½(6)(4)
= 12cm2
x 2
24cm2 5 h
SA = LA + BA
= 192cm2 + 24cm2
= 216cm2
a2 + b2 = c2
h = 52
h = 4 3 6

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

8. 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

9. 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

10. What did I learn today?? Find the area of the lateral faces 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!