MENSURATION OF POLYHEDRAL SOLIDS

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MENSURATION OF POLYHEDRAL SOLIDS
PRISM

PYRAMID
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MENSURATION OF POLYHEDRAL SOLIDS
PRISM
Definition Identification
Lateral Total surface area
Volume
PYRAMID
Definition Identification
Lateral Total surface area
Volume
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MENSURATION OF POLYHEDRAL SOLIDS
TARGET AUDIENCE
STUDENTS OF CLASS 9-10
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LEARNING OBJECTIVES
After interacting with this software a learner
will be able to
Identify define prism,pyramid.
Differentiate between prism,pyramid
Calculate surface area of prism,pyramid.
Calculate volume of prism,pyramid.
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DEFINITION OF POLYHEDRON
For example
Prism ,Pyramids ,Cubes ,Tetrahedron
Tetrahedron
Pyramid
Cube
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POLYHEDRON
In general for every polyhedron

• Lateral surface area Perimeter of base height

• Volume Area of base height

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RIGHT PRISM
A right prism is a solid formed by plane faces
such that its bases are parallel and congruent
polygons, while the lateral faces are all
rectangles.
Lateral faces
base
edge
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RIGHT TRIANGULAR PRISM
In right triangular prism base is equilateral
triangle height is the distance between two
bases.
Lateral surface area Perimeter of base X height
a side of base
h height of prism
L.S.A. 3a h
Base is
a
Equilateral triangle
h
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RIGHT TRIANGULAR PRISM
Whole Surface Area
L.S.A. 2 (Area of base )
Whole surface area (Perimeter of base) X h 2
( Area of base)
a²
a²
W.S.A. 3a h
2
a
a
h
h
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RIGHT TRIANGULAR PRISM
Whole Surface Area
L.S.A. 2 (Area of base )
Whole surface area (Perimeter of base) X h 2
( Area of base)
a²
a²
W.S.A. 3a h
2
a
a
h
h
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RIGHT TRIANGULAR PRISM
Whole Surface Area
L.S.A. 2 (Area of base )
Whole surface area (Perimeter of base) X h 2
( Area of base)
a²
a²
W.S.A. 3a h
2
a
a
h
h
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RIGHT TRIANGULAR PRISM
Whole Surface Area
L.S.A. 2 (Area of base )
Whole surface area (Perimeter of base) X h 2
( Area of base)
a²
a²
W.S.A. 3a h
2
a
a
h
h
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RIGHT TRIANGULAR PRISM
Whole Surface Area
L.S.A. 2 (Area of base )
Whole surface area (Perimeter of base) X h 2
( Area of base)
a²
a²
W.S.A. 3a h
2
a
a
h
h
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RIGHT TRIANGULAR PRISM
Volume
Area of base X height
a²
h
V
4
a
a
h
h
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RIGHT TRIANGULAR PRISM
Volume
Area of base X height
a²
h
V
4
a
a
h
h
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RIGHT TRIANGULAR PRISM
Volume
Area of base X height
a²
h
V
4
a
a
h
h
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RIGHT TRIANGULAR PRISM
Volume
Area of base X height
a²
h
V
4
a
a
h
h
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RIGHT TRIANGULAR PRISM
Volume
Area of base X height
a²
h
V
4
a
a
h
h
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RIGHT TRIANGULAR PRISM
Volume
Area of base X height
a²
h
V
4
a
a
h
h
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PYRAMID
A Pyramid is a solid figure formed by plane faces
one of which called the base, is any rectilinear
figure , the rest are triangles having a common
vertex at a point outside the plane of the base.
vertex
Triangular face
Rectilinear base
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RIGHT PYRAMID
In right pyramid line segment OG joining vertex
to the centroid of the base ,is perpendicular to
the base ABC.
O
OG is the height(h) of the pyramid.
OM is the slant height(l),the length of the
line segment joining the mid-point of any side of
base.
h
l
B
M
G
A
a
C
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RIGHT PYRAMID
Lateral Surface Area
½(Perimeter of base X Slant Height)
O
L.S.A.3a
l
2
h
l
B
Where a Side of Base l Slant height
M
G
A
a
C
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RIGHT PYRAMID
Total Surface Area
L.S.A. Area of base
O
T.S.A.3a
a²
l
4
2
h
l
B
Where a Side of Base l Slant height
M
G
A
a
C
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RIGHT PYRAMID
Volume
1/3 (Area of base X Height)
O
a²
h
V
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h
l
B
Where a Side of Base h Perpendicular height
M
G
A
a
C
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ACKNOWLEDGEMENTS
Sh. V. K. Sodhi
Sh. Naresh Kapoor
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