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.