Findthe area of trapezium PQRS with hight PQ given in the below figure
Answers
Answer:
find the area of the trapezium PQRS with height PQ. where SR is 13m, RQ is 7m and PS is 12m and the value of PQ is unknown. 1. See answer ... Classify the following as finite or infinite set.
Step-by-step explanation:
Answer:114mx^{2}
Step-by-step explanation:
We have, trapezium PQRS, in which draw a line RT perpendicular to PS.
Where side, ST = PS – TP = 12 – 7 = 5m
[
∵
T
P
=
P
Q
=
7
m
]
I
n
r
i
g
h
t
a
n
g
l
e
d
Δ
S
T
R
(
S
R
)
2
=
(
S
T
)
2
+
(
T
R
)
2
[
b
y
u
s
i
n
g
P
y
t
h
a
g
o
r
a
s
]
⇒
(
13
)
2
=
(
5
)
2
+
(
T
R
)
2
⇒
(
T
R
)
2
=
169
−
25
⇒
(
T
R
)
2
=
144
∴
T
R
=
12
m
[taking positive square root because length is always positive]
N
o
w
,
a
r
e
a
o
f
Δ
S
T
R
=
1
2
×
T
R
×
T
S
=
1
2
×
12
×
5
=
30
m
2
[
∵
a
r
e
a
o
f
t
r
i
a
n
g
l
e
=
1
2
(
b
a
s
e
×
h
e
i
g
h
t
)
]
Now, area of rectangle
P
Q
R
T
=
P
Q
×
R
Q
=
12
×
7
=
84
m
2
[
∵
a
r
e
a
o
f
r
e
c
t
a
n
g
l
e
=
1
2
(
l
e
n
g
t
h
×
b
r
e
a
d
t
h
)
]
[
∵
P
Q
=
T
R
=
12
m
]
∴
Area of trapezium = Area of DSTR + Area of rectangle PQRT = 30 + 84 = 114
m
2
Hence, the area of trapezium is 114
m
2
.
Alternate Method
Find TR as in the above method
∴
Area of trapezium =
1
2
(Sum of parallel lines)
×
Distance between two points
=
1
2
(
P
S
+
Q
R
)
×
T
R
=
1
2
×
(
12
+
7
)
×
12
=
1
2
×
19
×
12
=
114
m
2
Hence, the area of trapezium is
114
m
2
.