What is the perimeter of a semicircle?

Options

A. `pir`
B. `r(pi+2)`
C. `(2pir+1)r`
D. `2pir`

Answer

To find the perimeter of a semicircle, we can follow these steps:

### Step 1: Understand the components of a semicircle
A semicircle consists of two parts: the curved part (the arc) and the straight part (the diameter).

### Step 2: Recall the formula for the circumference of a full circle
The circumference (perimeter) of a full circle is given by the formula:
\[ C = 2\pi r \]
where \( r \) is the radius of the circle.

### Step 3: Calculate the length of the curved part of the semicircle
Since a semicircle is half of a circle, the length of the curved part (arc) of the semicircle is half of the circumference of the full circle:
\[ \text{Length of the arc} = \frac{1}{2} \times 2\pi r = \pi r \]

### Step 4: Add the length of the diameter
The diameter of the semicircle is twice the radius:
\[ \text{Diameter} = 2r \]

### Step 5: Combine the lengths to find the perimeter
Now, we can find the perimeter \( P \) of the semicircle by adding the length of the arc and the diameter:
\[ P = \text{Length of the arc} + \text{Diameter} = \pi r + 2r \]

### Step 6: Factor out the radius
We can factor out \( r \) from the expression:
\[ P = r(\pi + 2) \]

### Conclusion
Thus, the perimeter of a semicircle is:
\[ P = r(\pi + 2) \]

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