On a rectangular plot, a horse is tied to a pole at a corner of a hut which measures 15 m by 5 m. The hut is at the centre of the rectangular grass patch and there is a 10 m wide border of grass patch around it. Given that the rope is 7 m long,

1. what is the maximum grass patch area that the horse can feed on?
2. find the total area of the grass patch that the horse cannot feed on. (Take π = 3.14)

(a)
Length of the rope that covers ³₄ of the big circle = 7 m
Length of the rope that covers the remaining area which is ¹₄ of the small circle
= 7 - 5
= 2 m

Maximum area that the horse can feed on
= (³₄ x π x 7 x 7) + (¹₄ x π x 2 x 2)
= 37.75π
= 118.535 m²

(b)
Length of the rectangular plot
= 15 + (2 x 10)
= 15 + 20
= 35 m

Breadth of the rectangular plot
= 5 + (2 x 10)
= 5 + 20
= 25 m

Area of the rectangular plot
= 35 x 25
= 875 m²

Area of the hut
= 15 x 5
= 75 m²

Area of the grass patch cannot be fed on
= 875 - 75 - 118.535
= 681.465 m²

Answer(s): (a) 118.535 m²; (b) 681.465 m²