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Byju's Answer
Standard VII
Mathematics
Construction of a Triangle with SSS Criterion
Find the area...
Question
Find the area of the triangle whose vertices are
(
8
,
4
)
,
(
6
,
6
)
and
(
3
,
9
)
.
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Solution
Let the
Δ
A
B
C
have vertices
A
(
x
1
,
y
1
)
=
(
8
,
4
)
,
B
(
x
2
,
y
2
)
=
(
6
,
6
)
and
C
(
x
3
,
y
3
)
=
(
3
,
9
)
.
Now
a
r
Δ
A
B
C
with vertices
A
(
x
1
,
y
1
)
,
B
(
x
2
,
y
2
)
and
C
(
x
3
,
y
3
)
is
a
r
Δ
A
B
C
=
1
2
[
x
1
(
y
2
−
y
3
)
+
x
2
(
y
3
−
y
1
)
+
x
3
(
y
1
−
y
2
)
]
∴
a
r
Δ
A
B
C
=
1
2
[
8
(
6
−
9
)
+
6
(
9
−
4
)
+
3
(
4
−
6
)
]
units
⇒
a
r
Δ
A
B
C
=
0
Therefore,
a
r
Δ
A
B
C
=
0
The points
A
,
B
and
C
are collinear, since
a
r
Δ
A
B
C
=
0
.
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1
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Q.
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(
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