Geometry

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# Perimeter of a Semicircle

## The Perimeter Formula

The formula for perimeter of a semicircle is given as:**P = r(π + 2)**

Where *P* is the perimeter and *r* is the radius.

### Where the Semicircle Formula Comes From

The formula is created by halving the circle perimeter formula (circumference) and adding the diameter length to that.

Perimeter of a full circle is P = 2πr, so half of that is πr, which gives us the top arc’s length for the semicircle. The bottom side of the semicircle is equal to the circle’s diameter, so it is 2r since d = 2r.

Adding the two components, we get P = πr + 2r. We factor out the *r* from both terms and get P = r(π + 2) as the final formula.

### Example Problems

**Problem 1:**

Find the perimeter of a semicircle with a diameter of 10.

Solution:

First, we need to find the radius.

r = d/2 = 10/2 = 5

Now we will plug the radius into the formula.

P = r(π + 2)

P = 5(π + 2) = 25.708**The perimeter is 25.708.**

**Problem 2:**

Find the perimeter of a semicircle with a radius of 8.

Solution:

Plugging the radius directly into the formula, we get:

P = r(π + 2) = 8(π + 2) = 41.133**The perimeter is 41.133.**

**Problem 3:**

A semicircle has a perimeter of 27. What is the radius?

Solution:

Let’s plug the perimeter into the formula and solve for radius.

P = r(π + 2)

27 = r(π + 2)

27/(π + 2) = r

r = 5.251**The radius is 5.251.**

Result :

Worksheet 1

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Cheat sheet

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