Area of a triangle formula
The most common way to find a triangle's area is half the base times the height. It works for any triangle, as long as the height is measured perpendicular to the chosen base.
What each symbol means
| Symbol | Meaning | Units |
|---|---|---|
| A | Area | square units |
| b | Base (any side) | length unit |
| h | Height perpendicular to the base | length unit |
Rearranged forms
Worked example
A triangle has a base of 6 and a height of 4. Find the area.
- Start from A = ½ b h.
- Substitute b = 6 and h = 4.
- Multiply: A = 0.5 × 6 × 4.
The height must be the perpendicular distance from the base to the opposite vertex, not the length of a slanted side. If you only know the three side lengths, use Heron's formula instead. Area comes out in square units.
Have a base and height, or three sides?
Enter your measurements and the Triangle Area Calculator finds the area by base-height or Heron's formula.
How the formula works
Any triangle is exactly half of a rectangle built on the same base and height. That is why the area is one-half base times height. The base can be any side, as long as the height is measured perpendicular to it.
Other ways to find the area
When you do not have the height, Heron's formula uses the three side lengths, and the trig form A = ½ a b sin C uses two sides and the angle between them. All give the same area; pick the one that matches what you know.
FAQ
What is the area of a triangle formula?
A = ½ b h: one-half the base times the perpendicular height. It works for every triangle.
What if I do not know the height?
Use Heron's formula with the three side lengths, or A = ½ a b sin C if you have two sides and the included angle.
Does the base have to be the bottom side?
No. Any side can be the base, as long as the height is the perpendicular distance from that side to the opposite corner.