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Question:

In the X-Y plane, the area of the region bounded by the graph of |x + y| + |x – y| = 4 is

Explanation:

|x + y| + |x – y| = 4         … (i)

Consider the case when x and y are both positive. This is the area of quadrant I.

In this case, two cases are possible.

Case I: x > y

In this case, expression (i) becomes:

x + y + x – y = 4

∴ 2x = 4

∴ x = 2

Case II: x < y

In this case, expression (i) becomes:

x + y + y – x = 4

∴ 2y = 4

∴ y = 2

∴ The area for the first quadrant is as shown in the figure.

Extending the same logic to other quadrants, we get the area as shown in the above diagram.

∴ Its area = 4 × 4 = 16 sq. units

Hence, option (c).