The problem is asking to find the perimeter of a regular pentagon. From the image, it's indicated that the pentagon has a side length of 27 mm and an apothem of 19 mm. Since it’s a regular pentagon, all its sides are equal.

Formula for the perimeter of a regular polygon:

$P = n \times s$ Where:

• $n$ is the number of sides (5 for a pentagon),
• $s$ is the side length (27 mm in this case).

Calculation:

$P = 5 \times 27 = 135 \text{ mm}$

Thus, the perimeter is 135 mm.

Would you like more details or have any questions?

Here are 5 related questions:

1. How would the formula change if this was a hexagon?
2. How can we calculate the area of the pentagon given the side length and apothem?
3. What is the relationship between the apothem and the perimeter in regular polygons?
4. How do you derive the perimeter for irregular polygons?
5. What would the perimeter be if each side was increased by 10%?

Tip: In regular polygons, knowing just one side length allows you to find the perimeter easily, since all sides are equal!