Question

The area enclosed within the curve $|x|+|y|=2$ is

• A. $16$ sq.units
• B. $24$ sq. units
• C. $32$ sq. units
• D. $8$ sq. units

Answer 1

The correct option is D $8$ sq. units

Four cases arise from the given equation.

$x+y=2$ when $x>0$ and $y>0$

$-x+y=2$ when $x<0$ and $y>0$

$-x-y=2$ when both x and y are $<0$

$x-y=2$ when $x>0$ and $y<0$

If you plot them you will get co-ordinates as

$(2,0)(0,2)(-2,0)(0,-2)$

Join them you will get a square of side equal to $2\sqrt{2}$ units.

Thus area enclosed= Area of square=$(2\sqrt{2}{)}^2$

=$8$ sq.units