Discussion
The area of region bounded by the straight lines \(|x| + |y| = 1\) is :
Answer: B
The area is 2 square units.
The graph of \(|x| + |y| = 1\) is a square with its corners on the axes at (1, 0), (0, 1), (-1, 0) and (0, -1), a square standing on one corner. Its diagonals both have length 2, and the area of a rhombus or square is half the product of its diagonals:
\[ \text{Area} = \tfrac{1}{2} \times 2 \times 2 = 2 \]
Equivalently, it is made of four right triangles of legs 1 and 1, each of area 1/2. An answer of 4 comes from taking the square from -1 to 1 on both axes, whose corners lie outside the region, and 1 counts only half of it.
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