At each corner of a triangular field of sides 26 m, 28 m and 30 m, a cow is tethered by a rope of length 7 m, the area (in m²) ungrazed by the cows is

Solution (By Examveda Team)

$$\eqalign{ & {\text{Area Grazed by the cow}} \cr & = \frac{{{A^ \circ }}}{{360}}\pi {\left( 7 \right)^2} + \frac{{{B^ \circ }}}{{360}}\pi {\left( 7 \right)^2} + \frac{{{C^ \circ }}}{{360}}\pi {\left( 7 \right)^2} \cr & = \pi {\left( 7 \right)^2}\left[ {\frac{{{A^ \circ } + {B^ \circ } + {C^ \circ }}}{{360}}} \right] \cr & = \pi {\left( 7 \right)^2} \times \frac{{180}}{{360}} \cr & = \frac{1}{2}\pi {\left( 7 \right)^2} \cr & = 77{\text{ }}{{\text{m}}^2} \cr & s = \frac{{26 + 30 + 28}}{2} = 42 \cr & {\text{Area of field}} = \sqrt {s\left( {s - a} \right)\left( {s - b} \right)\left( {s - c} \right)} \cr & = \sqrt {42 \times 16 \times 14 \times 12} \cr & = 336{\text{ }}{{\text{m}}^2} \cr & \Rightarrow {\text{Remaining area}} = 336 - 77 = 259{\text{ }}{{\text{m}}^2} \cr} $$