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Find the area of the region bounded by graph

(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)


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