Determine the perimeter of a regular polygon whose one side measures 24 cm and each central angle is 24 degrees.

To determine the perimeter of the regular polygon, we can follow these steps:

### Step 1: Determine the number of sides of the polygon
The central angle of a regular polygon is related to the number of sides by the formula:

\[
\text{Central Angle} = \frac{360^\circ}{n}
\]

where \(n\) is the number of sides of the polygon. We are given that the central angle is 24 degrees, so:

\[
24^\circ = \frac{360^\circ}{n}
\]

Solving for \(n\):

\[
n = \frac{360^\circ}{24^\circ} = 15
\]

So, the polygon has 15 sides.

### Step 2: Calculate the perimeter
The perimeter \(P\) of a regular polygon is given by the product of the number of sides and the length of one side:

\[
P = n \times \text{side length}
\]

Here, \(n = 15\) and the side length is 24 cm. Thus:

\[
P = 15 \times 24 = 360 \, \text{cm}
\]

### Final Answer:
The perimeter of the regular polygon is \(360\) cm.

Would you like more details on any part of the process?

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Here are 5 related questions to explore:

1. How is the formula for the central angle of a regular polygon derived?
2. If the central angle was halved, how many sides would the polygon have?
3. What is the sum of the interior angles of a regular polygon with 15 sides?
4. How do you calculate the area of a regular polygon?
5. What happens to the perimeter if the side length is doubled but the central angle remains the same?

**Tip:** Regular polygons with more sides closely approximate the shape of a circle.

Learn how to calculate the perimeter of a regular polygon with a side length of 24 cm and a central angle of 24°. This geometry problem explores the relationship between the central angle and the number of sides, using key formulas to find the solution. Suitable for students in Grades 7-9.

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