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

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  • $\begingroup$ The second, of course $\endgroup$ – Michael Rozenberg Jun 6 '20 at 3:46
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    $\begingroup$ what do you think? $\endgroup$ – Jackozee Hakkiuz Jun 6 '20 at 3:47
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    $\begingroup$ 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 $\endgroup$ – Mathsisfun Jun 6 '20 at 3:47
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    $\begingroup$ @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". $\endgroup$ – Blue Jun 6 '20 at 4:01
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    $\begingroup$ 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." $\endgroup$ – Blue Jun 6 '20 at 4:03
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(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.

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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.

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

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