How it is calculated
Base times height, divided by two. Heron’s formula uses the semiperimeter. When two sides and the included angle are known, the area is half the product of the sides and the sine of that angle.
S = √[p(p−a)(p−b)(p−c)]
Where the numbers come from
- What is known
- Base
- Height
- Side a
- Side b
- Side c
- Angle between the sides — unit in the field: °
Example
Sides 3, 4, and 5. Semiperimeter 6, area by Heron √(6×3×2×1) = 6.
Questions
Why does it say there is no triangle?
The sum of two sides must be greater than the third. 2, 3, and 10 do not close into a shape.
Is the angle in degrees or radians?
In degrees.
Does the height have to fall inside?
The “base and height” form also works for an obtuse triangle, if the height is measured to the line of the base.