Triangle area
For obtuse triangles, the perpendicular height can fall outside the triangle. The three-side method works for acute, right and obtuse triangles.
Enter dimensions in the same unit. Results are shown in square or cubic units. Geometric volume measures internal capacity only when the dimensions describe the interior.
Understand this calculator
A triangle’s area is the amount of two-dimensional space inside its three sides. You can calculate it using a base and perpendicular height, or use all three side lengths with Heron’s formula. Both methods work for acute, right and obtuse triangles.
How to use this calculator
- Three sides (Heron’s formula)
- Enter the lengths of sides a, b and c. No angle or height is required. The lengths must satisfy the triangle inequality: each pair of sides must add to more than the third.
- Base and perpendicular height
- Enter the base and the shortest perpendicular distance from that base line to the opposite vertex. For an obtuse triangle, this height may lie outside the triangle itself.
Formula and method
In the first formula b is the base and h is the perpendicular height. In Heron’s formula a, b and c are the three side lengths, and s = (a+b+c) ÷ 2 is the semiperimeter.
Worked example: a 3–4–5 triangle
For sides 3, 4 and 5, the semiperimeter is s = (3+4+5) ÷ 2 = 6. Heron’s formula gives √(6 × 3 × 2 × 1) = √36 = 6 square units. Using base 4 and perpendicular height 3 gives ½ × 4 × 3 = 6 square units as well.
Understanding the results
- Area
- The result is expressed in square units: for example, measurements in metres give square metres (m²).
- Triangle validity
- Three positive numbers form a non-degenerate triangle only when each side is shorter than the sum of the other two.
- Obtuse triangles
- The base–height formula still works. An obtuse angle changes where the perpendicular height is drawn, not the area formula.
Assumptions and common mistakes
- Sloping side versus height
- A sloping side is not automatically the perpendicular height.
- Mixed measurement units
- Convert every input to the same length unit before calculating.
- Impossible triangles
- Lengths such as 2, 3 and 6 cannot make a triangle and should not produce a valid area.
Frequently asked questions
Can I find the area of an obtuse triangle?
Yes. Use the three side lengths with Heron’s formula or use a base and its perpendicular height.
What if I know only two sides?
Two side lengths alone are generally insufficient. You also need an included angle, a height or another independent measurement.
Why is the result squared?
Area measures a surface. Multiplying two lengths produces units such as cm² or m².