L7 : Area of Triangle - Perimeter and Area, Mathematics, CBSE Class 7 Video Lecture

hello friends this video on perimeter
and area part 7 is brought to you by
example comm no more pure from exam so
now that we know how to find out area of
a parallelogram rectangle square can't
get in guess how can we find out the
area of a triangle now obviously it's
written on the screen that the area of
the triangle would be half the area of a
parallelogram while so that's because
whenever you look at the parallelogram
you would see that a diagonal will
always divide a parallelogram into two
triangles let's see if you draw a
diagonal like this so this diagonal
would divide this parallelogram into two
triangles this is triangle one
this is triangle - so triangle one and
two now you look at it very closely you
would see that these two triangles are
again congruent
how are they congruent that's because
this side is equal to this side which
are opposite sides of parallelogram
similarly this side is equal to this
side which is which are again opposite
sides of parallelogram and this is a
common side so by side-side-side
congruence these two triangles would be
contouring
now since triangle 1 and triangle 2 are
congruent that means area of triangle 1
will be equal to area of triangle 2
length so the area of this triangle will
be equal to area of this triangle what
does that means that means that area of
one of these triangles would be half of
the area of this parallelogram so that
is what we said here that area of a
triangle is 1/2 of area of a
parallelogram and what is area of a
parallelogram which we just now derived
in the previous slide the area of a
parallelogram is base into height so
therefore what is the area of a triangle
area upper triangle is half into base
into height now let us name this
parallelogram and let us try to find out
the areas of the two triangles let's say
this ABCD is a parallelogram so if I ask
you to find out the area of triangle a B
D so what would be the area of triangle
a B D so now this area of triangle a B D
this triangle would be half into base
into height so which one do you want to
consider as the base here
so here you can consider a B as base or
you can consider a D as Ben please let's
say that we considered a B as the base
so if a B is the base in that case what
would be height height would be the
perpendicular drawn on a b a b means
either a b or extended arm of a B so if
you draw a perpendicular and a B from
the opposite side which is this side so
this is how the perpendicular is let's
say this is e so half into base into
height would be D so in this way you can
find out the area of triangle a B B now
how about area of triangle
D C D so in this case also the same
thing half into base so in this case if
you assume this is the base that is C D
then what would be the height the
perpendicular which is drawn on CD from
the opposite side so what is that
perpendicular it could be this
perpendicular drawn from B on this side
let's say this is f so this would be C B
into B M so in this way you can find out
the area of the triangles now let us
assume that for the same parallelogram
if you divide it in this fashion let's
say this is your parallelogram son just
to drawing a rough diagram just to
explain you let's say instead of this
diagonal if you divide this
parallelogram like this so in that case
you have a b c d so you have triangle
ABC and triangle ACD
so what would be the area of triangle a
B C so in this case let us assume that
BC is the base so half into base that is
piece
hi it would be perpendicular drawn on DC
from the opposite vertex so let us call
this a so this would be a e similarly
what would be the area of triangle ACB
that would again be half into base into
height so let us say the base here is a
B so what would be the height of
perpendicular which is drawn on a B that
is the base from the opposite vertex so
let us call this point as f so this
would be happen to Indian to see if so
in this pattern we find out the area of
a triangle which is given by half into
base into height so now when they talk
about triangles you might be thinking
that in case of triangles we have many
different types of triangles like we
have certain triangles which are right
angle to angle that is they have a right
angle within them some tangles are
scalene triangles where all the sides
are of different lengths sometimes some
triangles are equal at run once where
all the sides are equal so now this part
we know how to find out the area of a
triangle will it hold true for all types
of travels well this formula holds true
for any type of triangle do you know why
that's because if you look at any
triangle you would see that if you take
a middle image of that triangle and
place them in front of each other they
make a parallelogram because how did we
derive the formula for area of triangle
we just derived it saying that it is
half the area of parallelogram so this
relationship between a triangle and a
parallelogram holds true for all types
of triangles so here on the screen you
see three different types of triangles
so one is the right angle triangle like
this one is a right angle triangle one
is a scalene triangle the other one is
an isosceles triangle so we have a
variety of triangles here and for each
of these you would notice their mirror
image so for this triangle so this would
be the mirror image which which will
coincide with this part but at the same
time it is laterally inverted like as
you see here so this is the mirror image
now
look at this overall diagram what it is
it is nothing but a parallelogram
similarly look at this one so here also
if you taste mirror image of this
triangle you see that the two triangles
make a parallelogram and the same holds
true here as well so this was also a
parallelogram so you see opposite sides
are equal and parallel so this is also a
parallelogram so since every triangle
and it's mirror image makes a
parallelogram therefore the formula of
triangle that is half into base into
height holds true for all types of
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