In a triangle ABC, AB + BC = 7·1 cm, BC + CA = 12·1 cm and CA + AB = 7·2 cm. What is the area of the triangle?

Adding all three: 2(AB + BC + CA) = 26.4, so perimeter = 13.2 cm, semi-perimeter s = 6.6 cm. Then CA = s − AB·side: AB = s − (BC+CA) = 6.6 − 12.1 = −5.5 (negative). This is impossible — the triangle is degenerate. Rechecking: AB = (7.1 + 7.2 − 12.1)/2 = 2.2/2 = 1.1, BC = (7.1 + 12.1 − 7.2)/2 = 12/2 = 6, CA = (12.1 + 7.2 − 7.1)/2 = 12.2/2 = 6.1. Sides: 1.1, 6, 6.1. Check triangle inequality: 1.1 + 6 = 7.1 > 6.1 ✓. By Heron's: s = 6.6, area = √[6.6 × 5.5 × 0.6 × 0.5] = √[10.89] ≈ 3.3. So area = 3.3 square cm.