Let us consider ABCD be a rectangular field.
Given, Length of the field = \[20\] m
Given, Breadth of the field = \[16\] m
From the given question,
A cow is tied with a rope at a point A.
Let us consider length of rope be AE = \[14\] m = l.
We know that Angle subtended at the centre of the sector = \[{{90}^{\circ }}\]
Now for Angle subtended at the center (in radians) \[\theta \] = \[90\pi /180\] = \[\pi /2\]
∴ Area of a sector of a circle = \[\frac{1}{2}{{r}^{2}}\theta \]
= \[\frac{1}{2}\times {{(14)}^{2}}\times (\pi /2)\]
= \[154\] \[{{m}^{2}}\]
Therefore, the area of the field in which cow can graze is \[154\] \[{{m}^{2}}\]