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Given:

a x + b y + c = 0; x, y ≥ 0 … (1)

-a x + b y + c = 0; x < 0 y ≥ 0 … (2)

-a x – b y + c = 0; x < 0 y < 0 … (3)

a x – b y + c = 0; x ≥ 0 y < 0 … (4)

To find:

The area of the figure formed by the lines a|x| + b|y| + c = 0

Explanation:

The given lines can be written separately in the following way:

a x + b y + c = 0; x, y ≥ 0 … (1)

-a x + b y + c = 0; x < 0 y ≥ 0 … (2)

-a x – b y + c = 0; x < 0 y < 0 … (3)

a x – b y + c = 0; x ≥ 0 y < 0 … (4)

The lines and the region enclosed between them is shown below.

So, the area of the figures formed by the lines a |x| + b |y| + c = 0 is

Square units