Mathematics · Class 9
Heron's Formula
Area of triangles using Heron's formula and applications.
3 sections15–25 min read6 MCQs · 2 examples
Chapter Overview
Heron's formula finds the area of a triangle when all three sides are known — without needing height. It uses semi-perimeter s = (a + b + c)/2 and is essential for triangular land and field problems.
Heron's Formula
Semi-perimeter
s = (a + b + c) / 2
Area
Area = √[s(s − a)(s − b)(s − c)]
Applications
- Use when only three sides are given
- Works for all types of triangles
- Combine with unit conversion in word problems
- Check triangle inequality before applying
Solved Examples
Step-by-step solutions — read each step before checking the final answer.
Example 1: Scalene triangle
Find area of triangle with sides 3 cm, 4 cm, 5 cm.
- 1s = (3 + 4 + 5)/2 = 6
- 2Area = √[6(6−3)(6−4)(6−5)]
- 3= √[6 × 3 × 2 × 1] = √36 = 6
Answer
Area = 6 cm²
Example 2: Equilateral triangle
Side of equilateral triangle is 10 cm. Find area.
- 1s = (10 + 10 + 10)/2 = 15
- 2Area = √[15 × 5 × 5 × 5]
- 3= √1875 ≈ 43.3 cm²
Answer
≈ 43.3 cm²
Key Points to Remember
- ✓ All three sides must be known
- ✓ Units of area are square units
- ✓ 3-4-5 triangle is right-angled with area 6
Exam Tips
- • Calculate s first and show substitution
- • Keep surds exact unless asked to approximate
- • Verify sides satisfy triangle inequality
Practice MCQs — Heron's Formula
Test your understanding with topic-wise multiple choice questions. Explanations appear after each answer.
Question 1 of 6Score: 0/0
Heron's formula needs: