# How to find the perimeter of a half circle?

#### Understand the Problem

The question is asking how to calculate the perimeter of a half circle, which involves understanding the formula for the circumference of a full circle and then adapting it for a half circle while also considering the straight edge of the diameter.

r(\pi + 2)

The final perimeter of the half circle is $r(\pi + 2)$.

#### Steps to Solve

1. Calculate the circumference of a full circle

Firstly, calculate the circumference of a full circle using the formula:

$$C = 2\pi r$$

where $r$ is the radius of the circle.

1. Calculate half of the circumference

Since we need the perimeter of a half circle, halve the circumference calculated in step 1:

$$C_{\text{half}} = \pi r$$

1. Add the diameter of the circle

The perimeter of the half circle includes half of the circumference as well as the diameter (which is equal to twice the radius, $d = 2r$). Therefore, add the diameter to the half circumference:

$$P = \pi r + 2r$$

1. Simplify the final expression

Combine the terms to get the final perimeter:

$$P = r(\pi + 2)$$

The final perimeter of the half circle is $r(\pi + 2)$.

The perimeter of a half circle combines both the curved edge and the straight edge (diameter), making it slightly more than half the circumference of a full circle.

#### Tips

A common mistake is forgetting to add the diameter when calculating the perimeter of the half circle. Always ensure both the curved part and the straight edge are included.

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