The area of the region represented by `|x-y| le 3 " and " |x+y|le 3`, is

Options

A. 36 sq. units
B. 18 sq. units
C. 72 sq. units
D. 6 sq. units

Explanation

To find the area of the region represented by the inequalities \( |x - y| \leq 3 \) and \( |x + y| \leq 3 \), we can follow these steps:

### Step 1: Rewrite the inequalities without absolute values
The absolute value inequalities can be rewritten as:
1. \( |x - y| \leq 3 \) implies:
- \( x - y \leq 3 \)
- \( x - y \geq -3 \)

2. \( |x + y| \leq 3 \) implies:
- \( x + y \leq 3 \)
- \( x + y \geq -3 \)