TriArea
Triangle Area Calculator
Area = ½ · base · height. Simple and fast.
Triangle area from base and height
Area is half the base times the perpendicular height. The height must be measured at right angles to the base, not along a sloping side.
| Base | Height | Area |
|---|---|---|
| 4 | 3 | 6.00 |
| 6 | 5 | 15.00 |
| 10 | 8 | 40.00 |
| 12 | 9 | 54.00 |
| 15 | 10 | 75.00 |
| 20 | 12 | 120.00 |
Using a sloping side instead of the perpendicular height is the single most common mistake here, and it always overstates the area. For an obtuse triangle the height may fall outside the triangle entirely, which is legitimate - extend the base line and measure to it. If you know all three sides but no height, use Heron's formula instead, which the triangle calculator applies. Doubling either the base or the height doubles the area; doubling both quadruples it.
Works for any triangle shape
As long as you use the perpendicular height (not a slanted side), ½·base·height gives the correct area regardless of whether the triangle is right, acute, obtuse, or scalene.
Common real-world use
Roof gables, triangular flags and banners, and cutting fabric or wood on the diagonal all rely on this exact formula.
Frequently asked questions
How do I find the height of a triangle?
If you know the area and base: height = 2 × Area / base. If you know two sides and the included angle: height = side × sin(angle). For a right triangle, one leg is automatically the height when the other is the base.
Can I use any side as the base?
Yes. Any side can be the base — just make sure you use the perpendicular height to that specific side. The area is the same regardless of which side you choose as the base. Pick whichever combination of base and height you actually know.
What if I only know the three sides?
Use Heron's formula: compute the semi-perimeter s = (a + b + c) / 2, then Area = √(s(s−a)(s−b)(s−c)). For sides 3, 4, 5: s = 6, Area = √(6×3×2×1) = √36 = 6. This works for any triangle.
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Last updated: September 6, 2026