Calculate the total area of the region enclosed by the absolute value graphs y = |x| − 1 and y = −|x| + 1.

Calculate the total area of the region enclosed by the absolute value graphs y = |x| − 1 and y = −|x| + 1.

• A. 2
• B. 4
• C. 1
• D. 3

Answer: A) 2

Explanation: The region is a square rotated by 45 degrees (a diamond) with vertices at (1,0), (0,1), (−1,0), (0,−1). Diagonals are 2 and 2. Area = 1/2 × d1 × d2 = 1/2 × 2 × 2 = 2 sq units.