Q) A stable owner has four horses. He usually tie these horses with 7 m long rope to pegs at each corner of a square shaped grass field of 20 m length, to graze in his farm. But tying with rope sometimes results in injuries to his horses, so he decided to build fence around the area so that each horse can graze.

Based on the above, answer the following questions :
(i) Find the area of the square shaped grass field.
(ii) (a) Find the area of the total field in which these horses can graze.
OR
(b) If the length of the rope of each horse is increased from 7 m to 10 m, find the area grazed by one horse. (Use p = 3.14)
(iii) What is area of the field that is left ungrazed, if the length of the rope of each horse is 7 cm?

Find the area of the unshaded region shown in the given figure.

Ans:

(i) Area of the grass field:

The grass field is square shaped and the area of a square is given by: A = (Side)2

∵ Given Side of the filed = 20 m

∴ Area of the field = (20)2 = 400 m2

Therefore, the Area of square shaped field is 400 m2

(ii) (a) Area grazed by all horses:

Since, each horse grazes in a quarter of a circle shaped field of radius 7 m (length of the rope)

∴ Area grazed by 4 horses = 4 x area grazed by one horse

= 4 x π (R)2

= π (R)2

= π (7)2 = 49 π

= 49 x

= 7 x 22 = 154 m2

Therefore, the Area of square shaped field is 400 m2

(ii)(b) Area grazed by one horse with 10 m rope:

∴ Area grazed by a horse = π (R)2

= π (R)2

= π (10)2

= π

= 25 π

= 25 x

=

= 78.57 m2

Therefore, the Area grazed by one horse is 78.57 m2

(iii) Area of ungrazed field:

Area left ungrazed =Total area of the field – Area grazed by 4 horses (tied with 7m rope)
= 400 – 154 = 246 m2

Therefore the Area left ungrazed is 246 m2 .

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