Question

A horse is tied to a peg at one corner of square shaped grass field of side 25 cm by means of a 14 m long rope. Find the area of the part of the field in which the house can graze. (take pie=22/7)​

Answer 1

• let AB is the grass field and a horse is tied at one corner by a 14 m long rope.

• Area of the part of the field in which the horse can graze is quadrant AEF of radius 14cm and angle of 90°

and we know that

$\boxed{ \bold{area \: of \: quadrant = \frac{ \theta}{360 \degree} \times \pi {r}^{2} }}$

$\bold{: \implies \cancel\frac{90}{360} \times \frac{22}{7} \times {14}^{2} } \: \: \: \: \\ \\ \bold{: \implies \frac{1}{4} \times \frac{22}{ \cancel7} \times 14 \times \cancel{14}} \\ \\ \bold{: \implies \frac{22 \times 14 \times \cancel 2}{ \cancel4} } \: \: \: \: \: \: \: \: \: \: \: \\ \\ \bold{: \implies \frac{22 \times 7 \times \cancel2}{ \cancel2} } \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ \\ \bold{: \implies 22 \times 7} \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ \\ \bold{: \implies \underline{154}} \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \:$

hence, 154 m² area of field can be grazed by the horse