Which of the following is a geometric measurement that can be derived from a radius?

Circumference is a geometric measurement that can be directly derived from the radius of a circle. The formula to calculate the circumference is given by the equation C = 2πr, where C represents the circumference and r is the radius. This relationship shows how the size of the circle is intrinsically linked to its radius, making it the most relevant measurement among the options provided.

The other options do not have this direct relationship with the radius of a circle. For instance, while a diagonal might relate to shapes like squares or rectangles, it is not defined by the radius of a circle. Perimeter is a term commonly associated with the total distance around a polygon and is not applicable to circles in the same sense as circumference. Height pertains to the vertical measurement of an object, which is unrelated to the concept of radius in circular geometry. This context reinforces the relevance of circumference as a key measurement linked directly to radius.