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MENSURATION OF POLYHEDRAL SOLIDS
PRISM
PYRAMID
&
MENSURATION OF POLYHEDRAL SOLIDS
PRISMDefinition & Identification
Lateral & Total surface area
Volume
PYRAMID
Definition & Identification
Lateral & Total surface area
Volume
TARGET AUDIENCE
MENSURATION OF POLYHEDRAL SOLIDS
STUDENTS OF CLASS 9-10
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.
A polygon is a two-dimensional shape bounded by straight line segments. Apolygon is said to be regular if the edges are of equal length and meet atequal anglesA polyhedron is a three-dimensional figure bounded by polygons
For example :
Prism ,Pyramids ,Cubes ,Tetrahedron
Pyramid CubeTetrahedron
DEFINITION OF POLYHEDRON
POLYHEDRON
In general for every polyhedron :
•Lateral surface area =Perimeter of base * height
•Volume =Area of base *height
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.
edge
base
Lateral faces
RIGHT TRIANGULAR PRISM
Equilateral triangle Base is
h
In right triangular prism base is equilateral triangle& height is the distance between two bases.
Lateral surface area = Perimeter of base X height
L.S.A. = 3a * ha
`a’ = side of base
`h’ = height of prism
RIGHT TRIANGULAR PRISM
h
a
L.S.A. + 2 (Area of base )
Whole surface area = (Perimeter of base) X h + 2 ( Area of base)
W.S.A. = 3a * h +32
a²
h
a
a²
Whole Surface Area
RIGHT TRIANGULAR PRISM
h
a
L.S.A. + 2 (Area of base )
Whole surface area = (Perimeter of base) X h + 2 ( Area of base)
W.S.A. = 3a * h +32
a²
h
a
a²
Whole Surface Area
RIGHT TRIANGULAR PRISM
h
a
L.S.A. + 2 (Area of base )
Whole surface area = (Perimeter of base) X h + 2 ( Area of base)
W.S.A. = 3a * h +32
a²
h
a
a²
Whole Surface Area
RIGHT TRIANGULAR PRISM
h
a
L.S.A. + 2 (Area of base )
Whole surface area = (Perimeter of base) X h + 2 ( Area of base)
W.S.A. = 3a * h +32
a²
h
a
a²
Whole Surface Area
RIGHT TRIANGULAR PRISM
h
a
L.S.A. + 2 (Area of base )
Whole surface area = (Perimeter of base) X h + 2 ( Area of base)
W.S.A. = 3a * h +32
a²
h
a
a²
Whole Surface Area
RIGHT TRIANGULAR PRISM
h
a
h
a
Area of base X height
V = 34
a² * h
Volume
RIGHT TRIANGULAR PRISM
h
a
h
a
Area of base X height
V = 34
a² * h
Volume
RIGHT TRIANGULAR PRISM
h
a
h
a
Area of base X height
V = 34
a² * h
Volume
RIGHT TRIANGULAR PRISM
h
a
h
a
Area of base X height
V = 34
a² * h
Volume
RIGHT TRIANGULAR PRISM
h
a
h
a
Area of base X height
V = 34
a² * h
Volume
RIGHT TRIANGULAR PRISM
h
a
h
a
Area of base X height
V = 34
a² * h
Volume
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
Rectilinear base
Triangular face
RIGHT PYRAMID
O
A
B
C
G
M
In right pyramid line segment OG joining vertex to the centroid of the base ,is perpendicular to the base ABC.
`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
a
RIGHT PYRAMID
O
A
B
C
G
M
h l
½(Perimeter of base X Slant Height)
Lateral Surface Area
L.S.A.=3a2
* l
Where a= Side of Basel= Slant height
a
RIGHT PYRAMID
Total Surface Area
O
A
B
C
G
M
h l
a
L.S.A. + Area of base
T.S.A.=3a2
* l +
Where a= Side of Basel= Slant height
3
4a²
RIGHT PYRAMID
O
A
B
C
G
M
h l
1/3 (Area of base X Height)
Volume
Where a= Side of Baseh= Perpendicular height
V = 3 a² * h12
a
