Three horses are tethered at 3 corners of a triangular plot of land having sides 20m, 30m and 40m each with a rope of length 7m.The area (in $$m^{2}$$) of the region of this plot, which can be grazed by the horses, is use ($$\pi$$=$$\frac{22}{7}$$)

let A = $$ \theta 1^\circ $$

     B =  $$ \theta 2^\circ $$    

    C = $$ \theta 3^\circ $$

area which can be grazed by 3 horses = sum of the areas of 3 sectors with central angles $$ \theta 1^\circ , \theta 2^\circ , \theta 3^\circ $$ and each with radius , r = 7 m

== $$ ( \pi r^2 \frac{ \theta 1}{360} + \pi r^2 \frac{ \theta 2}{360} + \pi r^2 \frac{ \theta 3}{360} ) m^2 $$

= $$\frac{\pi r^2}{360} (A + B + C) $$

A + B + C = 180 [sum of angles of triangle]

= $$ \frac{\pi r^2}{360} \times 180 = \frac{22}{7} \times 7 \times 7 \times \frac{180}{360} $$

           = 77 $$ m^2 $$