**(Q.)In the X-Y plane , the area of the region bounded by the graph of |x+y|+|x-y|=4 is**

(i)8

(ii)12

(iii)16

(iv)20

Solution:

For x ≥ 0, y ≥ 0 and x≥y

x+y+x-y=4 => 2x=4 =>x=2

For x ≥0, y ≥0 and x ≤y

x+y-x+y=4 =>2y=4 =>y=2

Area in the first quadrant =4

By symmetry(because both the parts separating + is inside modulus), total area in four quad=

4*4=16 Answer: (iii)