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Question 21
In the X-Y plane, the area of the region bounded by the graph of |x+y| + |x-y| = 4 is
Solution
If the moduli are removed, the equations formed are
x+y+x-y = 4 => x=2
x+y-x+y = 4 => y =2
-x-y+x-y = 4 => y=-2
-x-y-x+y = 4 => x=-2
The area enclosed by these equations is a square with vertices at (2,2), (-2,2), (-2,-2), (2,-2) as shown in figure.
The required area = 4*4 = 16
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