Question

A field is in the shape of a 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 $\Delta BEC,$

${BE}^2+{EC}^2={BC}^2{(90-30)}^2+{EC}^2={\left(100\right)}^2{EC}^2={\left(100\right)}^2-{\left(60\right)}^{2}EC=\sqrt{6400}=80m$
Now, ar trap. $ABCD=\frac{1}{2}(AB+CD)\times EC=\frac{1}{2}(90+30)\times 80=4800m^2$
Cost of ploughing $1m^2=$ Rs. $4$
Cost of ploughing $4800m^2=(4\times 4800)=$ Rs. $19200$