Heron's Formula — Flashcards
Karnataka Board · Class 9 · Mathematics
20 flashcards for Heron's Formula (Karnataka Board Class 9 Mathematics) to test yourself on key terms and facts.
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Find the area of a triangle with sides 3 cm, 4 cm, and 5 cm using 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…
A triangular plot has sides 13 m, 14 m, and 15 m. Find its area.
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…
Find the area of an equilateral triangle with side 6 cm using Heron's formula.
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…
The sides of a triangle are in ratio 3:4:5 and perimeter is 24 cm. Find the area.
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 …
State Heron's formula and explain what each variable represents.
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…
Find the area of triangle with sides 7 cm, 24 cm, and 25 cm. Verify it's a right triangle.
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 …
A triangle has perimeter 30 cm. Two sides are 8 cm and 12 cm. Find the area.
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] = √…
When should you use Heron's formula instead of ½×base×height?
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…
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Sources & Official References
- Karnataka SSLC — kseeb.kar.nic.in
- Dept of Pre-University Education, Karnataka
- National Education Policy 2020 — education.gov.in
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