← GSEB Class 9
Heron Formula
Chapter Overview
Herons formula finds the area of a triangle using only its side lengths, without needing the height. For a triangle with sides a, b, c, the semi-perimeter is s = (a + b + c)/2. The area = √(s(s-a)(s-b)(s-c)). This formula is especially useful for scalene triangles where the height is not easily determined. Applications include finding areas of irregular polygons by dividing them into triangles.
Topics Covered
- Semi-perimeter
- Heron Formula
- Area Calculation
- Scalene Triangles
- Area of Quadrilaterals
- Polygon Area via Triangles
Key Formulas
s = (a + b + c)/2
Area = √s(s-a)(s-b)(s-c)
Real-World Applications
Applications: Land surveying, irregular plot measurement, architecture, construction planning.
Study Tips
Tip: Memorize the Heron formula exactly
Tip: Practice with different triangle types
Tip: Apply to quadrilaterals by splitting into triangles