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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

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 $1 \mathrm{~m}^2$ of the field, find the total cost of ploughing the field.

Answers (1)

Solution.

Given, ABCD is trapezium having parallel side $AB = 90 m$, $CD = 30 m$

So, $B E=30 \mathrm{~m}$

Now, $A E=(A B-E B)$

$A E=(90-30) m$

$A E=60 \mathrm{~m}$

So, in the right triangle $\triangle \mathrm{AED}$

$
\begin{aligned}
& (A D)^2=(A E)^2+(D E)^2 \\
& (100)^2=(60)^2+(D E)^2 \\
& 10000=3600+(D E)^2 \\
& 10000-3600=(D E)^2 \\
& 6400=(D E)^2
\end{aligned}
$

Taking square root on both sides

$
\sqrt{6400}=\sqrt{(D E)^2}
$

$
D E=80 \mathrm{~m}
$

We know that the area of trapezium $A B C D=\frac{1}{2} \times($ sum of parallel sides $) \times$ height

$
\begin{aligned}
& =\frac{1}{2} \times(A B+C D) \times D E \\
& =\frac{1}{2} \times(90+30) \times 80 \\
& =120 \times 40=4800 \mathrm{~m}^2 \\
& \because \text { cost of ploughing } 1 \mathrm{~m}^2 \text { field }=\text { Rs } 4
\end{aligned}
$

$\therefore$ cost of ploughing $4800 \mathrm{~m}^2$ field $=4800 \times 4=$ Rs. 19200

Hence the total cost of ploughing the field is Rs. 19200.

 

Posted by

infoexpert21

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