# Does the perimeter of a semicircle include the diameter? [closed]

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

• The second, of course – Michael Rozenberg Jun 6 '20 at 3:46
• what do you think? – Jackozee Hakkiuz Jun 6 '20 at 3:47
• yes. it is $\pi r + d$ where $r$ is the radius and $d$ is the diameter because you add half of the perimeter of the circle to the diameter – Mathsisfun Jun 6 '20 at 3:47
• @TomMathew: 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 circular arcs, then it may be not-entirely-unreasonable to use "perimeter" to describe their lengths as a friendlier alternative to the stuffy-sounding "arc length". – Blue Jun 6 '20 at 4:01
• 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." – Blue Jun 6 '20 at 4:03

## 2 Answers

(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.

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 $$\frac{2\pi R}{2}+2R=\color{blue}{\pi R+2R}$$