Heron's Formula
Gujarat Board · Class 9 · Mathematics
Quick revision notes for Heron's Formula — Gujarat Board Class 9 Mathematics. Key concepts, formulas, and definitions for last-minute revision.
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Introduction to Heron's Formula
- Heron's Formula calculates triangle area using only the three side lengths
- It is used when height is unknown or difficult to calculate
- Named after Heron of Alexandria (10 AD), a Greek mathematician
Step-by-Step Application
- Step 1: Identify the three sides a, b, and c
- Step 2: Calculate semi-perimeter s = (a+b+c)/2
- Step 3: Find (s-a), (s-b), and (s-c)
Worked Examples and Applications
- Example 1: Triangle with sides 40m, 32m, 24m gives area 384 m²
- Example 2: Equilateral triangle with side 10cm gives area 25√3 cm²
- Example 3: Isosceles triangle with sides 8cm, 5cm, 5cm gives area 12 cm²
Special Cases and Variations
- Equilateral triangles: all sides equal, can use alternative formula
- Isosceles triangles: two sides equal, simpler calculations
- Right triangles: can verify using basic area formula
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