Question

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

• A. $8$
• B. $6$
• C. $4$
• D. none

Answer 1

The correct option is A $8$

Given equation is $|x|+|y|=2$

$⟹x+y=2,x\ge 0,y\ge 0$

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

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

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

These four lines form a square.

The intersection points $(0,2),(2,0),(0,-2),(-2,0)$ are the coordinates of the square as shown in the above figure.

The area of the square is $side\times side=(\sqrt{(0-2{)}^2+(2-0{)}^2}{)}^2=8$