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Mensurationaksa

This document discusses the mensuration of polyhedral solids, specifically prisms and pyramids. It defines prisms and pyramids, and provides formulas to calculate the lateral surface area, total surface area, and volume of right triangular prisms and right pyramids. For prisms, the lateral surface area is calculated as the perimeter of the base multiplied by the height. For pyramids, the lateral surface area is half the perimeter of the base multiplied by the slant height. The document is intended for students in classes 9-10 to help them learn about and calculate measurements of various 3D shapes.

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Aven Mhar
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63 views27 pages

Mensurationaksa

This document discusses the mensuration of polyhedral solids, specifically prisms and pyramids. It defines prisms and pyramids, and provides formulas to calculate the lateral surface area, total surface area, and volume of right triangular prisms and right pyramids. For prisms, the lateral surface area is calculated as the perimeter of the base multiplied by the height. For pyramids, the lateral surface area is half the perimeter of the base multiplied by the slant height. The document is intended for students in classes 9-10 to help them learn about and calculate measurements of various 3D shapes.

Uploaded by

Aven Mhar
Copyright
© © All Rights Reserved
We take content rights seriously. If you suspect this is your content, claim it here.
Available Formats
Download as PPS, PDF, TXT or read online on Scribd
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MENSURATION OF

POLYHEDRAL SOLIDS
PRISM
&
PYRAMID

MENSURATION OF
POLYHEDRAL SOLIDS
PRISM

Definition & Identification


Lateral & Total surface area
Volume
PYRAMID

Definition & Identification


Lateral & Total surface area
Volume

MENSURATION OF
POLYHEDRAL SOLIDS
TARGET AUDIENCE

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.

DEFINITION OF POLYHEDRON
A polygon is a two-dimensional shape bounded by straight line segments. A
polygon is said to be regular if the edges are of equal length and meet at
equal angles
A polyhedron is a three-dimensional figure bounded by polygons

For example :
Prism ,Pyramids ,Cubes ,Tetrahedron

Pyramid

Cube

Tetrahedron

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.
Lateral faces

base
edge

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
Equilateral triangle

a
h

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)

W.S.A. = 3a * h + 3 a
2

a
h

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)

W.S.A. = 3a * h + 3 a
2

a
h

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)

W.S.A. = 3a * h + 3 a
2

a
h

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)

W.S.A. = 3a * h + 3 a
2

a
h

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)

W.S.A. = 3a * h + 3 a
2

a
h

RIGHT TRIANGULAR PRISM


Volume
Area of base X height

V = 3 a * h
4

a
h

RIGHT TRIANGULAR PRISM


Volume
Area of base X height

V = 3 a * h
4

a
h

RIGHT TRIANGULAR PRISM


Volume
Area of base X height

V = 3 a * h
4

a
h

RIGHT TRIANGULAR PRISM


Volume
Area of base X height

V = 3 a * h
4

a
h

RIGHT TRIANGULAR PRISM


Volume
Area of base X height

V = 3 a * h
4

a
h

RIGHT TRIANGULAR PRISM


Volume
Area of base X height

V = 3 a * h
4

a
h

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

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.

B
M
A

RIGHT PYRAMID

Lateral Surface Area


(Perimeter of base X Slant Height)
O

L.S.A.=3a * l
2
Where
a= Side of Base
l= Slant height

B
M
A

RIGHT PYRAMID

Total Surface Area


L.S.A. + Area of base
O

T.S.A.=3a * l + 3 a
4
2
Where
a= Side of Base
l= Slant height

B
M
A

RIGHT PYRAMID

Volume

1/3 (Area of base X Height)


O

3
a * h
V=
12

Where
a= Side of Base
h= Perpendicular height

B
M
A

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