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

Answer: Option B

Solution

Answer: Option B

Solution:

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