Q1. Find the area of a triangle with sides 3, 4 and 5 cm.
s = (3 + 4 + 5)/2 = 6
Area = √[6(6−3)(6−4)(6−5)] = √[6×3×2×1]
Area = √36 = 6 cm²
Heron's Formula — Class 9
No height? No problem. Heron's formula gives a triangle's area straight from its three sides — compute it in one click.
Heron's formulaArea = √[s(s−a)(s−b)(s−c)], where a, b, c are the sides and s = (a+b+c)/2 is the semi-perimeter.
Semi-perimeters = (a + b + c)/2 — half the perimeter of the triangle.
When to use itUse it whenever you know all three sides but not the height (e.g. scalene triangles, quadrilaterals split into triangles).
Heron's formula calculator Interactive
Enter the three sides of a triangle to get the semi-perimeter and the area.
Semi-perimeter s—
Area—
The three sides must satisfy the triangle inequality (each side < sum of the other two), or the area comes out as "not a number".
Numericals practice Interactive
Triangle-area problems with steps.
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Solved examples
Formula sheet
| Quantity | Formula |
|---|---|
| Semi-perimeter | s = (a + b + c)/2 |
| Heron's formula | Area = √[s(s−a)(s−b)(s−c)] |
Common mistakes & exam wins
- Heron's formula needs only the three sides — no height and no angle.
- For a quadrilateral, split it into two triangles and add their areas.
- Always compute the semi-perimeter s first.
Frequently asked questions
What is Heron's formula?
Area = √[s(s−a)(s−b)(s−c)], where a, b, c are the sides and s = (a+b+c)/2 the semi-perimeter.
When do you use Heron's formula?
When all three sides of a triangle are known but the height is not.
What is the semi-perimeter?
Half the perimeter of the triangle, s = (a + b + c)/2.