Question

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

Answer 1

Step 1: Drawing the figure as per the given condition.

Step 2: Finding the area of the given sector.

As seen in the figure we need to find out the area of the sector AFEG whose radius is $14m$.

So, we know that the area of the sector

$AreaofsectorAFEG=\frac{\theta }{360°}\times {\mathrm{\pi r}}^2$

Here, $\theta =90°\&r=14m$

Putting the values in the formula

$\begin{array}{rcl}AreaofsectorAFEG& =& \frac{90°}{360°}\times \frac{22}{7}\times 14\times 14\\ & =& \frac{1}{4}\times 22\times 14\times 2\\ & =& 154m^2\end{array}$

Hence, the area of the field that can the cow can graze is $154m^2$