Area and Perimeter of Trapezium Video Lecture - CTET & State TET

hello friends this video on mensuration
part 2 is brought to you by exampie Oh
calm no more fear from exam let's talk
about a trapezium to watch a trapezium
to dissin also a port a lateral with one
pair of opposite sides parallel just one
pair of opposite sides are parallel
let's see if a DC d is a trapezium so in
this case we see that ad is parallel to
CD just one pair of sides are parallel
but if you look at ad and BC they are
not panelists only one pair of opposite
sides are parallel and this type of a
quadrilateral is called a trapezium now
you might wonder that how do we find out
the area of a trapezium because we have
never discussed about that before let's
see what do we do to find out this area
let's see what do we do to find out the
area of a check Needham see here in this
slide we will try to find out a general
formula for finding out TB of a
trapezium so that it becomes very easy
for us to find out area of any trapezium
whose dimensions are given let's see
here we have a b c d as the trapezium
where ad is parallel to B B okay now
what we do first of all our first step
would be to draw a perpendicular so we
draw a perpendicular from a from the
voltage a to the opposite side DT and we
draw another perpendicular from the
point D to the opposite side VB and
let's name these points as e and s
respectively ok so that's our first step
so what did we do first our first step
was to draw perpendicular a e and D F so
now what do we have now we have to find
out this entire green area right
now we have divided this green area into
three parts one is this Liezel a de so
now we have triangle a B II we have
another triangle d FC so we have
triangle d FC and we have this as the
middle we have this rectangle so what is
the rectangle it is rectangle a D and E
so now we have these three things now we
already know how to find out the area of
triangles and rectangles so maybe read
and make use of those knowledge now so
taking their poles that we divided it
into three different shapes and now let
us try to find out when third step we
find out area of each of these triangles
and rectangles so first area of triangle
a de so how do we find area of a
triangle half into base into height so
in this piece B it would be be e and
height would be AE so half into de into
AE now let us try to find out area of
triangle d SP so here also this would be
half into base into height so base would
be XV and height would be th so this
would be half into H P into D F and then
we find out the area of rectangle a d f
e so area of a rectangle is length into
brain so the length would be e s and the
bread would be DF or you can see a E
into e at anything is fine so net rate
is a into e so we have found out the
areas of all these three shapes
separated so now when you have to find
out the area of the trapezium so what
could be the area of the trapezium so
that would be equal to sum of these
three so if we call this as let's say a
we call this as B and if we call this NC
so area of trapezium would be given by a
plus B plus T so this is equal to half
into de into AE plus half into F P into
DF plus a into e a so this would be the
area of the Triplicane so now let us
denote the value 0 some values to each
of these lengths ok so here let us as
you own that the length of EF that is
the length of the rectangle is a so if F
is a then a B will also be in the quite
obvious let's assume that these
particulars that we have drawn they
they're males are a to the specific this
is 8 this will also be 8 right so now
let's put this values so we can write
half into de into AE is h plus half into
F P into DF is again H plus a e which is
again H into es which is a so therefore
this can be written and not here if you
compare these three terms you see that
half H is common is a common factor in
all the ten let's take out half H so VI
left with b e+ f c plus 2 a right to it
because half a half eight we have taken
outside but here there was no have to be
multiplied with two because they are
basically dividing it with two to be a
multi-language to advance so this can be
written as half h into de plus FC plus a
plus a this is how we can write it now d
e plus FC plus a so all these three
together upon what so this makes DC so
be
d + HC + a on a team together make b c
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so DC + a and what is a a is ad so this
is our final formula to find out the
area of trapezium that is half into H
that is height the perpendiculars into
some of the parallel sides that is DC +
ad so therefore we say that area of the
trapezium is given by half into hi into
some of the parallel sides now how about
finding the perimeter of a trapezium now
when it comes to parameter we know that
for any geometrical shape parameter is
always equal to sum of all the sides
like when we are talking about colleges
this polygons are made up of line
segment so sum of all the line segments
that form that polygon would be the
parameter now increase of trapezium many
different types of provisions exist for
example a trapezium with one angle equal
to 90 degree is a guide and vertically
whereas a tradition with the non
parallel sides equal for example this
side and this side a and non parallel
but if these non parallel sides are
equal in length then it is called an
unsocial stratagems if you have a
trapezium where the non parallel types
are unequal in length that will be a not
equal in length then that is a scalene
trapezium
so these are the three types of
trapezium that can exist now does not
matter which type of reptilian we are
talking about but very major opportunity
dream would always be equal to sum of
the four sides because a trapezium is
always made up of four sides and when it
comes to parameter it will just the
length of the boundary so that would be
some of the four side thank you please
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