2
You visited us
2
times! Enjoying our articles?
Unlock Full Access!
Byju's Answer
Standard X
Mathematics
Vertices of Plane Figures
Find the area...
Question
Find the area of region bounded by the triangle whose vertices are
(
1
,
0
)
,
(
2
,
2
)
,
(
3
,
1
)
using integration.
Open in App
Solution
Area of
△
A
B
C
=
Area of
△
A
B
D
+
Area of trapezium
B
D
E
C
−
Area of
△
A
C
E
A
r
e
a
A
B
D
Area ABD
=
∫
2
1
y
d
x
Equation of line between
A
(
1
,
0
)
B
(
2
,
2
)
is
y
−
0
x
−
1
=
2
−
0
2
−
1
y
x
−
1
=
2
y
=
2
(
x
−
1
)
Area ABD
=
∫
2
1
2
(
x
−
1
)
d
x
=
2
[
x
2
2
−
x
]
2
1
=
2
[
2
−
2
−
1
2
+
1
]
=
1
A
r
e
a
B
D
E
C
Area
B
D
E
C
=
∫
3
2
y
d
x
Equation of line between B(2,2) & C(3,1) is
y
−
2
x
−
2
=
1
−
2
3
−
2
y
−
2
=
−
(
x
−
2
)
y
=
4
−
x
Area BDEC
=
∫
3
2
(
4
−
x
)
d
x
=
[
4
x
−
x
2
2
]
3
2
=
4
(
3
−
2
)
−
1
2
(
3
2
−
2
2
)
=
4
−
1
2
×
5
=
3
2
A
r
e
a
A
C
E
Area ACE
=
∫
3
1
y
d
x
Equation of line between A(1,0) & C(3,1) is
y
−
0
x
−
1
=
1
−
0
3
−
1
y
x
−
1
=
1
2
y
=
1
2
(
x
−
1
)
Area ACE
=
∫
3
1
1
2
(
x
−
1
)
d
x
=
1
2
[
x
2
2
−
x
]
3
1
=
1
2
[
9
2
−
3
−
1
2
+
1
]
=
1
Hence,
Area of
△
A
B
C
=
Area of
△
A
B
D
+
Area of trapezium
B
D
E
C
−
Area of
△
A
C
E
=
1
+
3
2
−
1
=
3
2
Suggest Corrections
0
Similar questions
Q.
Using integration, find the area of the region bounded by the triangle whose vertices are
(
−
1
,
2
)
,
(
1
,
5
)
and
(
3
,
4
)
.
Join BYJU'S Learning Program
Grade/Exam
1st Grade
2nd Grade
3rd Grade
4th Grade
5th Grade
6th grade
7th grade
8th Grade
9th Grade
10th Grade
11th Grade
12th Grade
Submit
Related Videos
MATHEMATICS
Watch in App
Explore more
Vertices of Plane Figures
Standard X Mathematics
Join BYJU'S Learning Program
Grade/Exam
1st Grade
2nd Grade
3rd Grade
4th Grade
5th Grade
6th grade
7th grade
8th Grade
9th Grade
10th Grade
11th Grade
12th Grade
Submit
AI Tutor
Textbooks
Question Papers
Install app