Question

Four horses are tethered with equal ropes at 4 corners of a square field of side 70 m so that they just can reach one another. Find the area left ungrazed by the horses.

Answer 1

Given, side of a square = 70 m
Also, four horses are tethered with equal ropes at 4 corners of the square field.
Hence, each horse can graze upto 35 m of distance along the side.

$\therefore$ Area of the square field $=Side\times Side$
$=70\times 70=4,900m^2$
The grazed area in making a complete circle by taking all the four grazed parts.
So, area of grazed part $=\pi r^2$
$=\frac{22}{7}\times 35\times 35$
[$\because$ r = 35 m and taking $\pi$ = $\frac{22}{7}$]
$=22\times 5\times 35=3,850m^2$
Area left ungrazed by the horses
= Area of square field - Area of grazed part
= $4,900-3,850$
= $1,050m^2$