Question

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 $1m^2$ of the field, find the total cost of ploughing the field.

Answer 1

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 $\Delta BEC,(BC{)}^2=(BE{)}^2+(EC{)}^2$ [using Pythagoras theorem]
$\Rightarrow (100{)}^2=(60{)}^2+(EC{)}^2$
$\Rightarrow (EC{)}^2=10000-3600$
$\Rightarrow (EC{)}^2=6400$
$\therefore EC=\sqrt{6400}=80m$
[taking positive square root because length is always positive]
$\therefore$ Area of trapezium ABCD = $\frac{1}{2}\left(Sumofparallelsides\right)\times Distancebetweenparallelsides$
$=\frac{1}{2}(AB+CD)\times EC=\frac{1}{2}(90+30)\times 80$
$=\frac{1}{2}\times \left(120\right)\times 80=4800c{m}^2$
The cost of ploughing the field of $1m^2$ = Rs.4
$\therefore$ The cost of ploughing the field of 4800 $m^2$ = 4800 $\times$ 4 = Rs.19200
Hence, the total cost of ploughing the field is Rs.19200.