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Byju's Answer
Standard XII
Mathematics
Section Formula
Find the area...
Question
Find the area of the triangle formed by the points with polar coordinates
(
1
,
π
6
)
,
(
2
,
π
3
)
,
(
3
,
π
2
)
.
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Solution
With polar coordinates
(
a
,
θ
)
the point is
(
a
cos
θ
,
a
sin
θ
)
in
X
−
Y
coordinates
So the points
(
1
,
π
6
)
,
(
2
,
π
3
)
,
(
3
,
π
2
)
=
(
1
cos
30
°
,
1
sin
30
°
)
,
(
2
cos
60
°
,
2
sin
60
°
)
,
(
3
cos
90
°
,
3
sin
90
°
)
=
(
√
3
2
,
1
2
)
,
(
1
,
√
3
)
,
(
0
,
3
)
Area of triangle of vertices
(
x
1
,
y
1
)
,
(
x
2
,
y
2
)
,
(
x
3
,
y
3
)
is
1
2
∣
∣ ∣ ∣
∣
x
1
y
1
1
x
2
y
2
1
x
3
y
3
1
∣
∣ ∣ ∣
∣
1
2
∣
∣
∣
x
1
−
x
2
y
1
−
y
2
x
2
−
x
3
y
2
−
y
3
∣
∣
∣
=
1
2
∣
∣ ∣ ∣
∣
√
3
2
−
1
1
2
−
√
3
1
−
0
√
3
−
3
∣
∣ ∣ ∣
∣
=
1
2
∣
∣ ∣
∣
(
√
3
2
−
1
)
(
√
3
−
3
)
−
1
(
1
2
−
√
3
)
∣
∣ ∣
∣
=
1
2
(
3
2
−
√
3
−
3
√
3
2
+
3
−
1
2
+
√
3
)
=
1
2
(
4
−
3
√
3
2
)
=
(
2
−
3
√
3
4
)
sq. units
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Similar questions
Q.
The area of the triangle formed by the points given in the polar coordinate system
(
1
,
π
6
)
,
(
2
,
π
3
)
and
(
3
,
π
2
)
, is
Q.
State the following statement is True or False
The area (in sq. units) of the triangle formed by the points with polar coordinates
(
1
,
0
)
(
2
,
π
3
)
and
(
3
,
2
π
3
)
, is
5
√
3
4
Q.
Prove that the polar coordinates
(
0
,
0
)
,
(
3
,
π
2
)
, and
(
3
,
π
6
)
form an equilateral triangle.
Q.
The area of the triangle formed by points
(
0
,
0
)
(
3
,
π
2
)
a
n
d
(
3
,
π
6
)
is
Q.
Find the areas of the triangles the coordinates of whose angular points are
(
−
a
,
π
6
)
,
(
a
,
π
2
)
, and
(
−
2
a
,
−
2
π
2
)
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