A horse is placed for grazing inside a rectangular field 70 m by 52 m. It is tethered to one corner by a rope 21 m long. On how much area can it graze? How much area is left ungrazed?
Here the horse is tethered to one corner implies or means that the area available for grazing is a quadrant of radius 21 m. Now we need to find the area of this quadrant to find out the area available for grazing and then subtract it from the total area of the rectangular field to obtain the area left ungrazed.
Given length of rectangular field = ℓ = 70 m
Breadth of rectangular field = b = 52 m
∴ Area of the field = ℓ × b
⇒ Area of the field = 70×52
⇒ Area of the field = 3640 m2
We know in a rectangle all the angles are 90 degrees.
∴ Area available for grazing = area of quadrant
Where R = radius of circle & θ = central angle
Given R = 21 m and θ = 90°
Put the given values in the above equation,
(put π = 22/7)
⇒ Area available for grazing = 346.5 m2
Area left ungrazed = Area of field – Area available for grazing
⇒ Area left ungrazed = 3640 – 346.5
⇒ Area left ungrazed = 3293.5 m2
The area available for grazing is 346.5 m2 and area left ungrazed is 3293.5 m2.