Browse by Stream
QnA
Home
QnA
Go To Your Study Dashboard

Get Answers to all your Questions

header-bg qa
  • Home
  • NCERT
  • 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 1m^{2} of the field, find the total cost of ploughing the field.

Answers (1)

\left [ Rs. \; 19200 \right ]

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

                                                                                      

Draw DE parallel to CB

So, BE = 30 m

Now, AE = (AB - EB)

AE = (90 - 30) m

AE = 60 m

So, in right triangle \DeltaAED

\left ( AD \right )^{2}= (AE)^{2} + (DE)^{2} \: \; \; \; \; \; [Using Pythagoras theorem]

\left ( 100 \right )^{2}= (60)^{2} + (DE)^{2}

10000= 3600+(DE)^{2}

10000- 3600= (DE)^{2}

6400= (DE)^{2}

Taking square root on both sides

\sqrt{6400}= \sqrt{(DE)^{2}}

DE = 80 m

We\; know \; that\; the \; area \; of \; trapezium \; ABCD = \frac{1}{2} \times (sum \; of \; parallel \; sides) \times height

= \frac{1}{2} \times (AB+CD) \times DE

= \frac{1}{2} \times (90+30) \times 80

= 120\times 40= 4800\; m^{2}

\because \; cost \; of\; ploughing \; 1 m^{2} \; field = Rs \; 4

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

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

 

Posted by

infoexpert21

View full answer

Similar Questions

Latest Question