MENSURATION OF POLYHEDRAL SOLIDS PRISM PYRAMID &

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