the side of a quadrilateral taken in order are 5 m 12 metre 14 m 15 m respectively. the angle contained in the first two side is a right angle. find the area of the quadrilateral
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Answer:
In quad. ABCD, AB=5 m, BC= 12 m CD= 14m, DA = 15m and
∠
A
B
C
=
90
0
Join AC,
Now in right
Δ
A
B
C
,
A
C
2
=
A
B
2
+
B
C
2
=
(
5
)
2
+
(
12
)
2
=
25
+
144
=
169
=
(
13
)
2
∴
A
C
=
13
m
Now area of right
Δ
A
B
C
=
1
2
×
b
a
s
e
×
h
e
i
g
h
t
=
1
2
×
A
B
×
B
C
=
1
2
×
5
×
12
m
2
=
30
m
2
and in
Δ
A
C
D
, sides are 13m, 14m, 15m
∴
s
=
a
+
b
+
c
2
=
13
+
14
+
15
2
=
42
2
=
21
m
Now area of
Δ
A
C
D
=
√
s
(
s
−
a
)
(
s
−
b
)
(
s
−
c
)
=
√
21
(
21
−
13
)
(
21
−
14
)
(
21
−
15
)
=
√
21
×
8
×
7
×
6
.
=
√
3
×
7
×
2
×
2
×
2
×
7
×
2
×
3
.
=
7
×
3
×
2
×
2
=
84
m
2
∴
Area of quad. ABCD = 30+84=
114
m
2
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