Finding Area of Polygon Video Lecture | Mathematics & Pedagogy Paper 2 for CTET & TET Exams - CTET & State TET

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we look at quality so we have been
gradually knowing how to find out area
and parameter of many different
geometrical shapes let's talk about
quality so what is the polygon it is a
simple closed curve made out of only
line same let us look at some of the
closed curves and find out which are
polygons see here on the screen
you see some closed curve for example
the first one is rectangle so this is
the closed curve a simple curve as well
now what are the simple curve simple
version one which doesn't cross over
itself for example if you have a curve
like this so this is not simple because
at these points the third part is over
it set what it intersects itself so that
is not a simple curve but for a ponytail
they are all simple curves
simple car closed curves and here you
see the expander it was made up of four
line segments you just add this one it
is made up of six line segments look at
this one
here you have one two three four five
six seven eight nine ten eleven twelve
twelve line segments here you have three
zero five zero four and here you have
eight line segments so these are all
polygons which are made up of only line
segments and they are also simple closed
curve now the question is how do we find
out the area of a polygon so we have
already talked about quite a few
polygons for example the quadrilateral
under different types of quadrilaterals
we have also spoken about the triangles
let's now talk about a polygon with more
number of sides for example of Pentagon
that is with five sign so in this case
let us suppose a b c d e is a pentagon
and we have to find out the area of this
pentagon so what are we going to do
again we are going to create the help of
triangulation that is we are going to
divide
in the one in two triangles and then you
can find out the area of the triangle as
they must to get the edge of the
Pentagon so how do we draw how do we
translate this Pentagon so for that
again we will draw diagonals so let's
say that we draw the diagonal AP and AD
so the moment we draw diagonals so what
we did we draw diagonals AC and AD so
what what happened as a result of this
so as a result of this we've got three
triangles so what are the three
triangles triangle ABC triangle a-p-d
and triangle a d e so triangle number 1
2 & 3 so we obtain 3 triangles so now
what we need to do so now you need to
find out the area of these three
triangles sum them up to get the area of
the pentagon now in order to find out
the area of these triangles you would
definitely need to know the measurement
of the diagonals easy and easy because
area of each triangle would be half into
base into height right so beam would be
the diagonal and height would be the
perpendicular drawn on the diagonal
should ID these percentages we need it
so you would basically need the
measurement of the diagonals and also
the particulars or the diagonals so if
you have the one you would be able to
find out the area of the head ever so
this was our option number one so this
was option number one where we divided
the Pentagon's into three triangles
finding area and add them up but we also
have an option number two there we
divide the center one into such a way
that could be divided into three
triangles and one rectangle would you
like to see how okay for that for the
same Pentagon we draw a diagonal
this being so we draw de and then we
draw these perpendicular from the
vertices let me draw the perpendicular
from it we draw a perpendicular from
steel and we also draw a perpendicular
from P so basically in the second option
we draw de and we also draw
perpendicular from point A C and B on D
so we draw one diagonal and then we draw
perpendicular from all the remaining
three vertices on that diagonal so once
we do that what happens be basically any
of dividing it into three triangles and
one rectangle so what are the three
triangles triangles a d-ii triangle C D
G what is G let's call this point as G
and let's call this point as H let's
call this point as a so triangle le de
the top triangle the triangle TDG
District this portion this triangle is
TD G similarly you have this triangle
which is b e:h traveled
de8 plus we have one rectangle
what is that rectangle it is cd8 G so
basically you have one triangle to
triangle triangle the top region with
one angle this whole thing is one
triangle and then you have this
remaining portion which is a rectangle
so how do you find out the area of the
Pentagon some of the areas of these
three triangles plus district tangents
now all these it is not necessary that
this would be a rectangle
in this case the paint upon that we have
completed it against a quite unique on a
regular center one now you might have
sentiments like these as well for
example here in this case if the
Pentagon is like this so in that case
even if you draw de and then you draw
the perpendicular from all the other
three vertices what will you get you get
one tangent a de 1000 C F D let's call
this and G let's call this as H so you
basically get three triangles and one
trapezium so this centre region in this
case is not a rectangle instead this is
a strategy so in this case how will you
find out the area of the vector area of
triangle a de señor crandall de plus the
area of triangle C D F plus area of
triangle D G in plus area of the
trapezium C D G F so this is how you
would find out the area of the
spend-down one similarly if you have a
contaminated here also if you look at
this portion this is not a rectangle why
how do we know this is not a rectangle
you see the opposite sides are not
parallel
therefore the all angles are not equal
to 90 degree and therefore it is not a
rectangle so this is again a Trekkie D
then this is also in a similar way we
can find out the area of the Pentagon so
basically the concept is that whenever
you are given a positon you need to make
use of triangulation
so that you can divide it into triangles
and rectangles or trapezium and then I
know they're in here add them up to get
the area of the polygon so let us look
at a hexagon now now a hexagon can be a
regular hexagon that is a hexagon with
all the three sides equal in length or
it could be an irregular xl1 where all
the six sides are not equal they are of
different lengths so in case of my
regular X I want your job becomes
simpler what you're going to do is just
join the
and te so the moment you draw these two
tracker these two lines what happens you
end up dividing it into two triangles
and one rectangle so therefore the area
of the XR bond would be area of triangle
a B F plus area of triangle Dec plus
area of the rectangle D s-e-c so it is
back simple so that way we can find out
any of the dreaded an example now when
it comes to the image lnx a bond in that
case water reduce here also we joined
the F here also we join te but in this
case the difference is that all that you
get in between that is not a rectangle
so this is basically a trapezium these
two sides are parallel but these two
sides are not parallel this BN is not
parallel to C so in this case this is a
trapezium so therefore here is there a
area of the hexagon will be given by
area of triangle a DX plus area of
triangle BCE plus area of the trapezium
DC e f so here is drift I am trying to
give you an idea that even if you are
given a qualitative doesn't matter
hounding science just try to draw
diagonal and divide it into triangles or
rectangles and sexism and then find out
their individual area some blame us to
get the area of the polygon
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