Triangle Area Calculator
Calculate the area of a triangle using base and height, or three sides (Heron's formula). Instant results with step-by-step explanation.
Area
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These sides cannot form a valid triangle.
Triangle Area Formulas
A = ½ × base × height
Heron's Formula:
s = (a + b + c) / 2
A = √(s(s−a)(s−b)(s−c))
Heron's Formula:
s = (a + b + c) / 2
A = √(s(s−a)(s−b)(s−c))
Example 1 (Base & Height):
Base = 10, Height = 6
A = ½ × 10 × 6 = 30 square units
Example 2 (Heron's Formula):
Sides: a=5, b=6, c=7
s = (5+6+7)/2 = 9
A = √(9×4×3×2) = √216 ≈ 14.6969 square units
Base = 10, Height = 6
A = ½ × 10 × 6 = 30 square units
Example 2 (Heron's Formula):
Sides: a=5, b=6, c=7
s = (5+6+7)/2 = 9
A = √(9×4×3×2) = √216 ≈ 14.6969 square units
When to Use Each Formula
| Method | Use When |
|---|---|
| Base & Height | You know the base length and perpendicular height |
| Heron's Formula | You know all three side lengths |
Frequently Asked Questions
What is the height of a triangle?
The height (or altitude) is the perpendicular distance from the base to the opposite vertex. It must form a 90° angle with the base.
Can Heron's formula work for any triangle?
Yes, Heron's formula works for any valid triangle — scalene, isosceles, or equilateral — as long as the three sides satisfy the triangle inequality (sum of any two sides must exceed the third).
What is the triangle inequality?
For three sides to form a valid triangle, the sum of any two sides must be greater than the third: a+b > c, a+c > b, and b+c > a.
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Last updated: 2026-08-08