# Formula for the perimeter of a semicircle

#### Understand the Problem

The question is asking for the mathematical formula used to calculate the perimeter (or circumference) of a semicircle, which includes both the curved part and the diameter.

$\pi r + 2r$

The perimeter of a semicircle is given by the formula $\pi r + 2r$, where $r$ is the radius of the circle.

#### Steps to Solve

1. Understand the components of the semicircle perimeter

The perimeter of a semicircle consists of the curved part (half of the circumference of a full circle) and the diameter.

1. Calculate the circumference of the full circle

The circumference of a full circle is given by the formula:

$$C = 2 \pi r$$

where $r$ is the radius of the circle.

1. Calculate the curved part of the semicircle

Since the semicircle is half of the full circle, the curved part is:

$$\text{Curved part} = \frac{1}{2} \times 2 \pi r = \pi r$$

1. Add the diameter to the curved part

The diameter of the circle is twice the radius, given by:

$$D = 2r$$

Therefore, the perimeter of the semicircle is:

$$\text{Perimeter} = \pi r + 2r$$

The perimeter of a semicircle is given by the formula $\pi r + 2r$, where $r$ is the radius of the circle.