How this calculation works
The height must be measured at a right angle to the chosen base. It is not generally the sloping side of the triangle.
Area = base × perpendicular height ÷ 2A worked example
A base of 10 and perpendicular height of 6 gives an area of 30 square units.
Good to know
Uses the stated formula and assumptions. Displayed decimal values are rounded; use consistent units for all inputs.
A sloping side is usually not the height
The formula uses the perpendicular distance from the chosen base to the opposite vertex. A sloping edge may look like a height in a drawing, but using it directly generally overstates the area.
The perpendicular can even land outside the triangle when the triangle is obtuse. The area formula still works: the relevant measurement is the distance to the line containing the base, not necessarily an internal segment.
Why the rectangle formula gets divided by two
Two matching copies of a triangle can form a parallelogram with the same base and perpendicular height. The triangle occupies half of that parallelogram’s area. This explains the factor of one half without treating it as an arbitrary rule.
If you know three side lengths but not a height, this is not the appropriate input model. Find a justified height or use a method designed for the available side data.
A few questions, answered
Can I use any side as the base?
Yes, provided you use the perpendicular height corresponding to that particular base.
What if the height is zero?
The computed area is zero, representing a degenerate flat triangle.