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Question 5
A field is in the shape of trapezium having parallel sides 90m and 30m. These sides meet the third side at right angles. The length of the fourth side is 100m. If it costs Rs.4 to plough 1m2 of the field, find the total cost of ploughing the field.

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Solution

In trapezium ABCD, we draw a perpendicular line CE to the line AB.

We have, DC = AE = 30m
Now, BE = AB – AE = 90 – 30 = 60m
In right angled ΔBEC, (BC)2=(BE)2+(EC)2 [using Pythagoras theorem]
(100)2=(60)2+(EC)2
(EC)2=100003600
(EC)2=6400
EC=6400=80m
[taking positive square root because length is always positive]
Area of trapezium ABCD = 12(Sum of parallel sides)×Distance between parallel sides
=12(AB+CD)×EC=12(90+30)×80
=12×(120)×80=4800 cm2
The cost of ploughing the field of 1m2 = Rs.4
The cost of ploughing the field of 4800 m2 = 4800 × 4 = Rs.19200
Hence, the total cost of ploughing the field is Rs.19200.


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