A cow is tied with a rope of length 14 m at the corner of a rectangular field of dimensions 20 m × 16 m. Find the area of the field in which the cow can graze.

Question

Philoid · Accepted Answer

Let ABCD be a rectangular field.

Length of field = 20 m

Breadth of the field = 16 m

Suppose a cow is tied at a point A.

Let length of rope be AE = 14 m = l (say).

Angle subtended at the center of the sector = 90°

Angle subtended at the center (in radians) θ = 90π/180 = π/2

∴ Area of a sector of a circle

= 154 m²

Hence, the required area of a sector of a circle is 154 m^2.