Question

A grassy field has the shape of an equilateral triangle of side $6$ m. A horse is tied to one of its vertices with a rope of length $4.2$ m. The percentage of the total area of the field which is available for grazing is best approximated by

• A. $50\%$
• B. $55\%$
• C. $59\%$
• D. $62\%$

Answer 1

The correct option is C $59\%$

Given, side of an equilateral triangle $=6$ m

Area of equilateral triangle
$=\frac{6\times 6\times \sqrt{3}}{4}=9\sqrt{3}$ sq. m
$=9\times 1.73=15.57$
Area that can be grazed (sector)
$=\frac{60}{360}\times \frac{22}{7}\times \frac{42}{10}\times \frac{42}{10}$
$=9.24$ sq. m
Required $\%$ $=\frac{9.24}{15.57}\times 100\%$ $=59\%$