What is a radian of a triangle?

A radian is defined as the angle subtended at the center of a circle by an arc that is equal in length to the radius of that circle. This means that one radian represents an angle formed when the radius is bent along the circumference of the circle.

In the context of triangles, while radians are not specific to triangles alone, they are a crucial concept when discussing the angles within any geometric shape, including triangles. Using radians for measuring angles is particularly beneficial in trigonometry because it allows for easier calculations with functions like sine, cosine, and tangent, especially when working within the unit circle.

The other answer choices do not accurately define what a radian is. The measurement of area, specific angle calculations in degrees, and distance measures around a triangle do not pertain to the concept of a radian. Hence, defining a radian as a unit of rotation equal to the angle subtended at the center is the only accurate description among the provided options.