Area of General Quadrilateral, Area of Special Quadrilaterals, Rhombus Video Lecture - Class 8

hello children in this lesson we are
going to find area of quadrilateral so
in our last lessons we have learnt how
to find area of square rectangle
triangle etc right for example here is a
rectangular field it's area is length
into breadth right but in real life when
we see different figures like this is a
house or a building with nice glass here
or this is another building we find lot
of shapes which are not just rectangle
square but the quadrilateral right that
is rectangle or square are also caught a
little but they have specific properties
like square as all the four sides same
and all the four angles also 90 degree
but here there is a quadrilateral with
four sides but here not all sides are
same size right so let us try to find
out how do we find the area of an any
gender recorder later so as we can see
this quadrilateral if we have to find
its area that is the inner part of it we
can break it this quadrilateral or we
can think this quarter later less two
triangles one triangle this and another
triangle this so here is a diagonal of
this quadrilateral going from one vertex
to another if we can find the area of
this triangle in area of this triangle
if we join them we are going to get the
entire area of quadrilateral right so
the quadrilateral with vertex ABC and D
can be thought as a quadrilateral with
two triangles triangle ABC and triangle
AC D right and if we can find the area
of this triangle ABC plus area of
triangle ACD we sum them we are going to
find the area of this entire
quadrilateral right AC is the diagonal
BD can also be a diagram in that case we
can use the triangles areas trying a BD
plus CB d either base you can find it
and we know area of triangle is what
it's half base into height right so let
us try for this triangle ABC we draw a
perpendicular line from vertex b to its
opposite line that is AC right so this b
is that line which is the height of this
triangle ABC and its base is AC the
diagonal of this quadrilateral right so
the triangle ABC area would be half B
into AC same way we draw a perpendicular
line from vertex D to this line AC this
is the right angle and we can say the
area of triangle ACD is half of base AC
and height DF right let's call these
heights as h1 and h2 so what will be the
area of entire quadrilateral we said
it's the sum of area of triangle ABC and
triangle ACD and the area of triangle
ABC is what half of base AC and height B
and for the triangle ACD it is half AC
the base and the height DF right so we
can write AC as the diagonal of the
quadrilateral right it's common and PS h
1 and DFS H 2 this side and as we can
see diagonal is common we can n half is
common we can take it out so the area of
any gender equality little is half the
length of its diagonal multiplied by H 1
plus h 2 and H 1 and H 2 are the
perpendiculars drawn from the opposite
of vertex to the diagonal so this is one
such perpendicular line and this is
another such perpendicular line meeting
at 88 90 degree this
90 degree this is also 90 degrees so
area of any general quadrilateral is
half its length of its diagonals
multiplied by two Heights H 1 and H 2
now let's take a very specific
quadrilateral called rhombus right
we know rhombus has all the four sides
equal it has one more property its
diagonals BD and OD
right they divide the meat at a central
point in such a way that a o is equal to
OC and b o is equal to AU d one more
interesting properties of rhombus is
this two diagonals are perpendicular to
each other that is they meet at 90
degree BD is perpendicular to a see what
it means if BD is perpendicular to AC
evenly b o or OB is also perpendicular
to AC and same way OD is perpendicular
to AC so if we have to find the area of
this rhombus all we need to do is find
the area of this triangle ABC and
triangle ADC
and if we sum them we get the area of
rhombus and what would that be half of
diagonal AC multiplied by both the
heights just like any quadrilateral we
heard right this side and this side
right so half of diagonal multiplied by
some of the heights h1 which is OB and
h2 which is OD right and we know in case
of rhombus these two together because
they both these perpendicular are going
to the same point this can be written as
B D so what is the final thing which is
coming as area of rhombus half of AC
multiplied by B D which is half of
product of its diagonals so in a general
code a little it is half into one of the
diagonal multiplied by
some of the heights opposite to it but
in case of a rhombus which is of same
length of all the four sides and where
the diagonals meet each other at ninety
degree there the area is half of product
of its diagonal that is half multiplied
by length AC which is one diagonal and
BD which is other diagonals so that's
all in this lesson children bye-bye