The side elevation of an object is in the shape of an trapezium. One of the angles of the trapezium is 90 degree and lengths of the parallel sides are 106mm and 52mm. If the length of the slant side is 90mm find the area of the trapezium
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A field is in the shape of a trapezium having parallel sides 90 m and 30 m. These sides meet the third side at right angles. The length of the fourth side is 100 m. If it costs Rs 4 to plough 1m
2
of the field, find the total cost of ploughing the field.
Medium
Solution
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Correct option is A)
LetthefieldintheshapeofatrapeziumbePQRSwherePS∥QRand∠P&∠Qare90
o
.
HerePS=90m,RQ=30m&SR=100m
Drawa⊥RTfrompointRontoSP.
NowRT=PQandRT∥PQ.
HenceST=90−30=60m
ApplyingPythagoras
′
Theoremin△STR,
TR=
(100
2
−60
2
)
=
(10000−3600)
=
6400
=80m
So,thePQ=heightofthetrapezium=80m
TheareaofthetrapeziumPQRS
=
2
1
×PQ×(RQ+SP)
=
2
1
×80×(90+30)
=40×120
=4800
Costofploughing1field=Rs4
∴Costofplouging4800field
=4×4800
=Rs19200
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