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Surface Area of Prisms and Cylinders
Area
The area of a shape is a measure of how much surface
the shape takes up.
Prisms & Cylinders
Polyhedron – a solid bounded by polygons (a 3D figure)
Prism – a polyhedron with two congruent parallel faces called bases
Cylinder – a solid with congruent circular bases that lie in parallel planes
base
radius
base

height
Lateral face (4)
base
base
Prisms are classified by the shapes of their bases
Rectangles
The perimeter of a rectangle with length l and width w can
be written as:
l
Perimeter = 2l + 2w
or
w
Perimeter = 2(l + w)
The area of a rectangle is given as:
Area = lw
Triangles
The area of a triangle is found by multiplying the base (b)
times the height (h) and dividing by 2 (or multiplying by ½):
Surface Area verses Lateral Area
of a Prism
The lateral area of a polyhedron or prism is the sum
of the area of its lateral faces (without getting the
area of the bases).
LA = Ph
P = Perimeter of the base
h = height of 3-D shape
base
Lateral face (4)
base
Surface Area verses Lateral Area
of a Prism
The surface area of a polyhedron or prism is the sum
of area of its faces (including the area of the bases).
SA = Ph + 2B
P = Perimeter of the base
h = height of 3-D shape
B = Area of the base
base
Lateral face (4)
base
Example
Find the Lateral Area and Surface Area of the prism.
Example
Find the Lateral Area and Surface Area of the prism.
The circumference of a circle
For any circle,
The Circumference is found through the formula:
C = πd
Inversely, if you have the circumference, you can find the
diameter through the formula:
circumference
diameter =
π
Formula for the area of a circle
We can find the area of a circle using the formula
Area of a circle = π × r × r
radius
or
Area of a circle = πr2
Surface Area verses Lateral Area
of a Cylinder
The lateral area of a cylinder is the area of its curved
surface.
LA =
2p rh
radius
base

height
base
r = radius of the base
h = height of 3-D shape
Surface Area verses Lateral Area
of a Cylinder
The surface area of a cylinder is equal to the sum of the
lateral area and the areas of the two bases.
SA =
2p rh + 2p r 2
radius
base

height
base
Scaling
If we scale the dimensions of a prism or any other 3D
figure, we are multiplying each dimension (length, width,
height, etc) by the scale factor.
For example, if we have the following figure and scale it by 2,
It’s new dimensions are 4 cm by 10 cm, by 20 cm
Homework
Page
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16-17, #6, 7
18, #11A-C
22, #24
59, #8-10
60, #11
61, #18-20, 22, 23