(i)
Let ABCD be square field
and length of rope, r = 10m
We need to find the area of the field which horse can graze, i.e. the area of sector QBP
As we know that in a square all angles are of 90°
Hence, ∠QBP = 90°
= 78.5 m2
Hence, the area of the field which horse can graze = 78.5 m2
(ii) the decrease in the grazing area if the rope was 5 m long instead of 10m
Length of rope is decreased to 5m
Area grazed by a horse now = Area of sector HBG
= 19.625 m2
So, the decrease in the grazing area
= Area of sector QBP – Area of sector HBG
= 78.5 – 19.625
= 58.875 m2