# Grazing Cows

I was getting late for the office, so I opened the throttle and let my motorcycle fly.

But all my hopes of reaching the office in time were dashed; I soon found myself at the tail of a traffic jam. The traffic snarl was caused by a herd of cows, which was crossing the road at a leisurely pace. I could do nothing but wait. But the sight reminded me of a trigonometric problem I had come across recently. Here it is:

Three cows are tethered at each corner of a triangular plot, which is fenced all around so that the cows cannot cross its boundaries. The lengths of the sides of the triangular plot are 20 metres, 30 metres, and 40 metres. The cows are tethered with ropes of 7-metre length each.

Please help me to find out the total area of the plot that can be grazed by the three cows. Also, please help me determine the area of the plot grazed by each cow.

• Union Public Service Commission - www.upsc.gov.in
• IIT-Kharagpur - www.iitkgp.ac.in
• Indian Statistical Institute - www.isical.ac.in
• Indian Institute of Technology Madras - www.iitm.ac.in
• Indian Institute of Management, Ahmedabad - www.iimahd.ernet.in
• Indian Institute of Mass Commission - www.iimc.nic.in
• IIT Bombay - www.iitb.ac.in