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Find the area of a quadrilateral ABCD in which AB = 3 cm, BC = 4 cm, CD = 4 cm, DA = 5 cm

and AC = 5 cm.

Answer:

First, construct a diagram with the given parameter

Now, apply the Pythagorean theorem in ΔABC

"hello students welcome to lito q a video
session
i am saf your maths tutor and question
for today is
find the area of quadrilateral abcd in
which a b is equal to 3 centimeter bc is
equal to 4 centimeter
cd is equal to 4 centimeter da is equal
to 5 centimeter
and ac is equal to 5 centimeter
so here if you consider quadrature abcd
it is a combination of two triangles
triangle abc and triangle adc
to find the sum quad the total area of
this quadrilateral you do some triangle
abc and
triangle adc's area
so first of all let us find the area of
the triangle abc
so area of
triangle abc that is the heading
to find area of triangle abc we need to
find semi perimeter first
so semi perimeter
is equal to 3 plus
4 plus 5
upon 2 which is s is equal to
3 plus 4 plus 5
12 upon 2 and that is 6
6 centimeter now you know formula of
area that is haron's formula
so as per heron's formula area can be
given by
root of
s
s minus a s minus
b and s minus c
this is the formula to find area of the
given triangle
so root of
s is 6
6 6 minus three
six minus four six minus five
root off
six into
three into two into one
that is 6 into 6 and that is 6 square
and hence finally you will get
root of that will be 6 centimeter
square that is our area of triangle abc
this a is
now we have found the area of triangle
abc now let us look for triangle adc
to find the area of triangle adc we have
to use the same method
so i'll rub it over here and continue
here
i'll give heading area of
triangle adc to find area of triangle
adc
we know the harrow's formula to find
area that is area of triangle
is equal to root of
s s minus a s minus b
s minus c
so as per haran's formula where s is the
semi perimeter
and abc are the sides of the triangle
here a is equal to
phi b is equal to 4 and c is equal to 5
so s can be given as a plus b plus c
upon 2 and that is 5
plus 4 plus 5
upon 2 so s value comes out to be
7 meter or it is 7 centimeter
so 7 centimeter is our semi perimeter
now you can find the area by using
heron's formula
to find area using harold's formula let
us do it over here
remember s is equal to 7 centimeter so
area of the triangle can be given by
root of
7 7 minus
5 7 minus 4
and 7 minus 5
so that is root of
7 into
2 into 3 into 2
so that comes out to be
2
under root of 21
and that is
one 9.16 centimeter square
so this is the area of
triangle adc
now we have two areas area of triangle
adc as well as area of triangle abc
we can sum this both area so area of
quadrilateral
a b c d is equal to
area off we will sum them up
triangle adc plus
triangle abc
so we have to sum their area now we will
do it over here
any area of quadrilateral
will be equal to area of both the inner
triangle
and that is 6 plus 9.16
that is centimeter square and hence
it is 15.16
centimeter square
so this is the required value for the
area
or you can approximate your answer round
it off
as 15.2 centimeter square
so that is our area of quadrilateral
abcd
if you have any query you can drop it in
our comment section and subscribe to
ledo for more such q a thank you for
watching
"

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