G.GMD.3 STUDENT NOTES WS #1/#2
1
THE PRISM
A prism is a polyhedron that consists of a polygonal region and its translated image in a parallel plane, with
quadrilateral faces connecting the corresponding edges.
A common misconception is that whatever face the prism is ‘sitting’ on is the base – that IS NOT HOW THE
BASE IS DETERMINED!! The base represents the two congruent opposite parallel faces. The height of the
prism is the perpendicular distance between the two congruent bases.
The stacking of congruent parallel cross sections allows us to create a formula for the volume of prism.
VolumePRISM = Bh, where B is the area of the base and h is the height of the prism.
PRISM VOLUME CALCULATION
The formula for the volume of a prism is quite simple. The capital B represents
the AREA of the base. This sometimes confuses students because they might use
the base of a triangle or the base of a trapezoid here instead of the AREA of the
base. It is for this reason that this B has been capitalized to distinguish it different
from b or b1. The height, h, refers to the height of the prism which is one of the
lateral sides if it is a right prism. This too is sometimes confusing because bases
will have heights as well.
Example #1
Example #2
Name: Cube
V = Bh
V = (Area of Square)(height)
V = (5)(5) (5)
V = 125 cm3
Name: Triangular Prism
V = Bh
V = (Area of Triangle)(height)
V = ½ (5)(8) (10)
V = 200 cm3
VPRISM = Bh
Example #3
Name: Rectangular Prism
V = Bh
V = (Area of Rectangle)(height)
V = (3)(4) (12)
V = 144 cm3
G.GMD.3 STUDENT NOTES WS #1/#2
2
Example #4
VPRISM = Bh
VPRISM = ( Area of Hexagon ) h
 1 
VPRISM =   ap   h
 2 
 1 

VPRISM =    (3 3)(36) 10
 2 

2
VPRISM = 540 cm
Name: Hexagonal Prism
Example #5
VPRISM = Bh
VPRISM = ( Area of Composite ) h
VPRISM = ( 24 + 4 )10
VPRISM = 280 cm 2
G.GMD.3 WORKSHEET #1
NAME: ____________________________ Period _______
1. The same rectangular prism is provided three times below but in each instance a DIFFERENT BASE has
been highlighted. Calculate the volume for each but change the base dimensions.
a)
b)
c)
What do you notice about the volumes of these three examples? Why didn’t changing the base change the
volume?
2. Determine the volume of the prisms. (Lines that appear perpendicular are perpendicular.)
a)
b)
c)
Volume = _____________
Volume = _____________
Volume = _____________
d)
e)
f)
Volume = _____________
Volume = _____________
Volume = _____________
g)
h)
i)
Volume = _____________
Volume = _____________
Volume = _____________
1
G.GMD.3 WORKSHEET #1
2
3. Determine the volume of the prism.
a) Equilateral Triangular Prism
b)
c) Regular Hexagonal Prism
Volume = _____________ (E)
Volume = _____________
Volume = _____________ (E)
d)
e) Oblique Prism
f) Regular Hexagonal Prism
Volume = _____________
Volume = _____________ (E)
Volume = _____________ (E)
g)
h)
i)
Volume = _____________ (E)
Volume = _____________ (2 dec.)
Volume = _____________
G.GMD.3 WORKSHEET #2
NAME: ____________________________ Period _______
1. Determine the volume of the following prisms.
(Lines that appear to be perpendicular are perpendicular and lines that appear to be parallel are.)
a)
b)
Volume = ______________
c)
Volume = ______________
d)
Volume = ______________
e)
Volume = ______________
f)
Volume = ______________
Volume = ______________
1
G.GMD.3 WORKSHEET #2
2
e)
f)
Volume = ______________
g)
Volume = ______________
h)
Volume = ______________ (E)
i)
Volume = ______________ (2 dec.)
j)
Volume = ______________
Volume = ______________ (E)
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G.GMD.3 WORKSHEET #7
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G.GMD.3 WORKSHEET #1
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G.GMD,3 WORKSHEET #2
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