Question

Area of the quadrilateral formed by the line $|x|+|y|=2$ is ?

• A. $8$
• B. $6$
• C. $4$
• D. None

Answer 1

The correct option is A $8$

$\left|x\right|+\left|y\right|=2$

Equation of lines are: $x\ge 0,y\ge 0,x+y=2$

$x\le 0,y\le 0,x+y=2$

$x\ge 0,y\le 0,x-y=2$

$x\le 0,y\ge 0,x-y=2$

Shape formed by these lines is a square

Intersection points $(0,2),(2,0),(0,-2),(-2,0)$

Area of square :, Side $AB=\sqrt{2^2+2^2}=\sqrt{4+4}=\sqrt{8}$

$=side\times side$

$=\sqrt{8}\times \sqrt{8}=8$ units