Derive Formulas of Surface Area – Right Prisms and Right
Cylinders
Definition of a Prism
A Prism is a solid having bases or ends that are parallel, congruent polygons and sides that are parallelograms.
http://dictionary.reference.com/browse/prism
Parts of a Right PrismThe bases are congruent and parallel
The lateral faces are the faces connecting the corresponding vertices of the bases
Lateral edges are the segments connecting the lateral faces
Different Right Prisms
All Prisms with a Right angle
Oblique PrismA prism that has lateral edges that are not
perpendicular to the bases.
Height vs. Slant Height
A way to show the surface of a Prism
A two Dimensional representation of a prism is called a net
H
W
H
L
W
Another way is adding all the faces and bases
The equation
S.A. = 2(W·H + W·L + H·L)
W = 4; L = 7; H = 5
166832..
3528202..
7574542..
AS
AS
AS
To find surface area of a rectangular prism
S.A. = 2(2 x 4) + 2(3 x 4) + 2(2 x 3)
S.A. = 2(8) + 2(12) + 2(6)
S.A. = 16+ 24+ 12
S.A. = 52
Let’s Derive Surface Area Prism
SA = 2lw + 2wh + 2lhSA = 2lw + h(2w + 2l)SA = 2 bases + h perimeter⋅
HPBAS 2..
Surface Area of a Right Prism Theorem 12.2
The Surface Area of a Prism is the sum of two base areas and the lateral face areas.
Lateral faces = Height times Perimeter
B is area of a base
P is perimeter of the base
H is height
HPBAS 2..
Right Prism Theorem
The Base is 4(7)= 28
Perimeter is 2(4)+2(7) = 22
Height is 5
S.A. = 2(28) + 22(5)
S.A. = 166
HPBAS 2..
Your Turn!!!• Find the surface area
The bases are 12x2
S.A. = 2B+PhS.A. = 2(12x2) + 28x7S.A. = 48+196S.A. =244 cm2
Perimeter = 24 + 4H= 7
The bases are (11x17)/2
Perimeter = 11 +17 +20H = 6
S.A. = 2B+PhS.A. = 2(11x17)/2+ 48x6S.A. = 187+ 288S.A. =475 cm2
Define of a Cylinder
A Prism with a circular base
The net of a Cylinder
Two circles and a Rectangle
The Surface Area of a Cylinder
2 Bases + Circumference times height
HCBAS 2..
12
42
4 2
H
C
Base
The Surface Area of a Cylinder2 Bases + Circumference times height
HCBAS 2..
12
42
4 2
H
C
Base
128..
9632..
128162..
AS
AS
AS
hrrAS 22.. 2
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