Does the perimeter of a semicircle include the diameter?

Question

Is the perimeter of a semicircle $(\pi)(\text{radius})$ or $(\pi)(\text{radius})+\text{diameter}$?

Answer 1

(Transferring from a comment.)

You'll find in mathematics that terminology can vary from author to author. (We can't even agree on whether the natural numbers include zero!)

Context is key. If someone shows a semicircular region and asks its perimeter, then the diameter would certainly need to be included. On the other hand, if someone is discussing a semicircular arc, then it may be not-entirely-unreasonable to use "perimeter" to identify its length, perhaps as a friendlier alternative to the stuffy-sounding "arc length".

To quote Lewis Carroll's Humpty Dumpty:

When I use a word, it means just what I choose it to mean—neither more nor less.

Answer 2

Notice, the semi-circle is one dimensional locus of points that forms half of a circle. It consists of diameter & half the circumference of a circle.

Hence the perimeter of a semi-circle is $$\frac{2\pi R}{2}+2R=\color{blue}{\pi R+2R}$$