Class 9 Maths – Heron’s Formula

10.1 Area of a Triangle – by Heron’s Formula

• Heron’s formula is used to find the area of a triangle when all three sides are known.
• Not dependent on height.

Formula:

For a triangle with sides a, b, c:

1. Calculate the semi-perimeter (s):

$$s = \frac{a + b + c}{2}$$s=2a+b+c​

2. Area (Δ) of triangle:

$$\text{Area} = \sqrt{s(s-a)(s-b)(s-c)}$$Area=s(s−a)(s−b)(s−c)​

Steps to Solve:

1. Find semi-perimeter $s$s
2. Substitute $a, b, c$a,b,c and $s$s in formula
3. Solve the square root to get area

Example:

• Triangle with sides a = 5, b = 6, c = 7
• Step 1: $s = (5+6+7)/2 = 9$s=(5+6+7)/2=9
• Step 2: Area = $\sqrt{9(9-5)(9-6)(9-7)} = \sqrt{9 × 4 × 3 × 2} = \sqrt{216} \approx 14.7$9(9−5)(9−6)(9−7)​=9×4×3×2​=216​≈14.7

Note:

• Works for any type of triangle: scalene, isosceles, or equilateral.
• For equilateral triangle: Area = $\frac{\sqrt{3}}{4} a^2$43​​a2

Quick Short Q&A (Most Possible)