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Byju's Answer
Standard IX
Mathematics
Triangles between Same Parallels
ABCD is a par...
Question
A
B
C
D
is a parallelogram.
X
a
n
d
Y
are mid-points of
B
C
a
n
d
C
D
respectively. Then area
(
Δ
A
X
Y
)
=
3
k
area(parallelogram
A
B
C
D
).Find k
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Solution
G
i
v
e
n
:
A
B
C
D
i
s
a
p
a
r
a
l
l
e
l
o
g
r
a
m
.
X
a
n
d
Y
a
r
e
m
i
d
−
p
o
i
n
t
s
o
f
B
C
a
n
d
C
D
r
e
s
p
e
c
t
i
v
e
l
y
.
S
i
n
c
e
X
a
n
d
Y
a
r
e
t
h
e
m
i
d
−
p
o
i
n
t
s
o
f
s
i
d
e
s
B
C
a
n
d
C
D
r
e
s
p
e
c
t
i
v
e
l
y
i
n
△
B
C
D
∴
X
Y
∥
B
D
a
n
d
X
Y
=
1
2
B
D
.
A
r
e
a
(
△
C
Y
X
)
=
1
4
a
r
e
a
(
△
D
B
C
)
=
1
8
a
r
e
a
(
p
a
r
a
l
l
e
l
o
g
r
a
m
A
B
C
D
)
.
.
.
.
(
1
)
[
S
i
n
c
e
a
r
(
△
D
B
C
)
=
1
2
a
r
e
a
(
p
a
r
a
l
l
e
l
o
g
r
a
m
(
A
B
C
D
)
]
P
a
r
a
l
l
e
l
o
g
r
a
m
A
B
C
D
a
n
d
△
A
B
X
a
r
e
b
e
t
w
e
e
n
t
h
e
s
a
m
e
p
a
r
a
l
l
e
l
s
A
D
a
n
d
B
C
a
n
d
B
X
=
1
2
B
C
∴
a
r
e
a
(
△
A
B
X
)
=
1
4
a
r
e
a
(
p
a
r
a
l
l
e
l
o
g
r
a
m
A
B
C
D
)
.
.
.
.
.
(
2
)
S
i
m
i
l
a
r
l
y
,
a
r
e
a
(
△
A
Y
D
)
=
1
4
a
r
e
a
(
p
a
r
a
l
l
e
l
o
g
r
a
m
A
B
C
D
)
N
o
w
,
a
r
(
△
A
X
Y
)
=
a
r
(
p
a
r
a
l
l
e
l
o
g
r
a
m
A
B
C
D
)
−
[
a
r
(
△
A
B
X
)
+
a
r
(
△
A
Y
D
)
+
a
r
(
△
C
Y
X
)
]
⇒
a
r
(
△
A
X
Y
)
=
a
r
(
p
a
r
a
l
l
e
l
o
g
r
a
m
A
B
C
D
)
−
(
1
4
+
1
4
+
1
8
)
a
r
(
A
B
C
D
)
a
r
(
A
X
Y
)
=
(
1
−
5
8
)
a
r
(
p
a
r
a
l
l
e
l
o
g
r
a
m
A
B
C
D
)
=
3
8
a
r
(
p
a
r
a
l
l
e
l
o
g
r
a
m
A
B
C
D
)
.
Suggest Corrections
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