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(A) The equation $|x+y|=2$ can be written as $x+y=2$ or $x+y=-2$.For $x+y=2$,the intercepts on the axes are $(2,0)$ and $(0,2)$.For $x+y=-2$,the inter

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$8$

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(A) The equation $|x+y|=2$ can be written as $x+y=2$ or $x+y=-2$.For $x+y=2$,the intercepts on the axes are $(2,0)$ and $(0,2)$.For $x+y=-2$,the intercepts on the axes are $(-2,0)$ and $(0,-2)$.These four points are $A(0,2)$,$B(2,0)$,$C(0,-2)$,and $D(-2,0)$.These points form a rhombus with diagonals of length $d_1 = 4$ (along the $y$-axis) and $d_2 = 4$ (along the $x$-axis).The area of a rhombus is given by $\frac{1}{2} 	imes d_1 	imes d_2$.Area $= \frac{1}{2} 	imes 4 	imes 4 = 8$ square units.

If the points of intersection of the coordinate axes and $|x+y|=2$ form a rhombus,then its area is

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