Question

If area enclosed by the curve $|x|+|y|\le k$ is $f\left(k\right)$ sq.unit, Then what will be the value of $\frac{f\left(10\right)}{100}$.

Answer 1

In the first quadrant
$\begin{array}{c}x\ge 0,y\ge 0\\ x+y\le k\end{array}$
In the second quadrant
$-x+y\le k$
square area
$\begin{array}{c}=(k\sqrt{2}{)}^2=2k^2\\ f\left(k\right)=2k^2\\ f\left(x\right)=2x^2\\ f\left(10\right)=2\times 100\\ \frac{f\left(10\right)}{100}=2\end{array}$