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.

Answer

$ \pi r + 2r $
Answer for screen readers

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.

More Information

The formula for the perimeter of a semicircle includes both the curved part and the diameter. It combines half the circumference of the circle and the diameter.

Tips

A common mistake is to forget to include the diameter when calculating the perimeter of the semicircle.

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