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 rupee `4` to plough `1` `m^(2)` of the field, find the total cost of ploughing the field.

Explanation

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",triangleBEC " "(BC)^(2)=(BE)^(2)+(EC)^(2)" "["using pythagoras theorem"]`
`rArr" "(100)^(2)=(60)^(2)+(EC)^(2)`
`rArr" "(EC)^(2)=10000-3600`
`rArr" "(EC)^(2)=6400`
`therefore" "EC=sqrt6400=80m`
`["taking positive square root because length is always positive"]`
`therefore" ""Area of trapezium" ABCD=(1)/(2)("Sum of parallel sides")xx"Distance between parallel sides"`
`=(1)/(2)(AB+CD)xxEC=(1)/(2)(90+30)xx80`
`=(1)/(2)xx(120)xx80=4800m^(2)`
`because"Cost of ploughing the field of 1"m^(2)`= "rupee " 4`
`because"Cost of ploughing the field of 4800"m^(2)`=4800xx4="rupee "19200`
Hence, the total cost of ploughing the field is rupee `19200`.