**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 m^{2 }

**Therefore, the Area of square shaped field is 400 m ^{2 }**

**(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 m^{2}

**Therefore, the Area of square shaped field is 400 m ^{2}**

**(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 m^{2}

**Therefore, the Area grazed by one horse is 78.57 m ^{2}**

**(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 m^{2 }

**Therefore the Area left ungrazed is 246 m ^{2 }.**

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