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Byju's Answer
Standard X
Mathematics
Area of a Triangle Given Its Vertices
In fig., the ...
Question
In fig., the area of triangle ABC (in sq. units) is:
A
15
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B
10
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C
7.5
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D
2.5
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Solution
The correct option is
B
7.5
Given: Coordinates of Point
A
(
1
,
3
)
,
B
(
−
1
,
0
)
and
C
(
4
,
0
)
Construction: Drop a perpendicular from
A
on
x
−
axis, which meets x-axis at
D
≡
(
1
,
0
)
Now in
Δ
A
D
C
,
A
D
=
3
,
D
C
=
3
Area of
Δ
A
D
C
=
1
2
×
D
C
×
A
D
=
1
2
×
3
×
3
=
9
2
c
m
2
Now in
Δ
A
D
B
,
A
D
=
3
,
D
B
=
2
Area of
Δ
A
D
B
=
1
2
×
D
B
×
A
D
=
1
2
×
2
×
3
=
3
c
m
2
Area of
Δ
A
B
C
=
Ara of
Δ
A
D
C
+
Area of
Δ
A
B
D
=
9
2
+
3
=
15
2
=
7.5
c
m
2
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