Question

Three horses are tethered at $3$ corner of a triangular plot having sides $20m$, $30m$ and $40m$ with rope of $7m$ length each. Find the area of his plot which can be grazed by the horses.

• A. $77m^2$
• B. $67m^2$
• C. $76m^2$
• D. $70m^2$

Answer 1

The correct option is A $77m^2$

We have,

$r=7m$ (sector radii)

$a=20m$, $b=40m$, $c=40m$

Area $=\frac{x^0}{{360}^0}\left({\pi r}^2\right)+\frac{y^0}{{360}^0}\left({\pi r}^2\right)+\frac{z^0}{{360}^0}\left({\pi r}^2\right)$

$=\frac{{\pi r}^2}{{360}^0}\left({180}^0\right)$

$=\frac{22}{7}\times \frac{{\left(7\right)}^2}{2}=77$ sq. m.

Hence, this is the answer.