Heron's Formula

Answer

Step 1: Calculate semi-perimeter s = (a+b+c)/2 = (3+4+5)/2 = 6 cm Step 2: Apply Heron's formula: Area = √[s(s-a)(s-b)(s-c)] Step 3: Substitute values: Area = √[6(6-3)(6-4)(6-5)] = √[6×3×2×1] = √36 = 6

Answer

Step 1: s = (13+14+15)/2 = 42/2 = 21 m Step 2: s-a = 21-13 = 8 m, s-b = 21-14 = 7 m, s-c = 21-15 = 6 m Step 3: Area = √[21×8×7×6] = √[7056] = 84 m² Answer: 84 m²

Answer

Step 1: For equilateral triangle, all sides = 6 cm Step 2: s = (6+6+6)/2 = 9 cm Step 3: s-a = s-b = s-c = 9-6 = 3 cm Step 4: Area = √[9×3×3×3] = √[243] = 9√3 cm² ≈ 15.59 cm² Answer: 9√3 cm²

Answer

Step 1: Let sides be 3x, 4x, 5x. Perimeter = 3x+4x+5x = 12x = 24 Step 2: x = 2, so sides are 6 cm, 8 cm, 10 cm Step 3: s = 24/2 = 12 cm Step 4: Area = √[12×(12-6)×(12-8)×(12-10)] = √[12×6×4×2] = √576

Answer

Heron's Formula: Area = √[s(s-a)(s-b)(s-c)] Where: a, b, c = sides of triangle s = semi-perimeter = (a+b+c)/2 Example: For triangle with sides 5,12,13: s = 15, Area = √[15×10×3×2] = 30 units²

Answer

Step 1: Check if right triangle: 7² + 24² = 49 + 576 = 625 = 25² ✓ (Right triangle) Step 2: s = (7+24+25)/2 = 28 cm Step 3: Area = √[28×21×4×3] = √[7056] = 84 cm² Verification: Area = ½×7×24 = 84 cm²

Answer

Step 1: Third side = 30 - 8 - 12 = 10 cm Step 2: Check triangle inequality: 8+10 > 12 ✓, 8+12 > 10 ✓, 10+12 > 8 ✓ Step 3: s = 30/2 = 15 cm Step 4: Area = √[15×(15-8)×(15-12)×(15-10)] = √[15×7×3×5] = √

Answer

Use Heron's formula when: • You know all three sides but not the height • Finding height is difficult or impossible • Working with scalene triangles Example: Triangle park with sides 40m, 32m, 24m He