
    Design an algorithm for an adaptive learning system that calculates the total boundary length of a regular star-shaped badge, which has 5 equal sides, where the length of each side adjusts based on student performance level. The system should compute the complete distance around the badge using the current side length value selected by the adaptive difficulty system.
    

    
import math

def perimeter_pentagon(a):
    """
    Design an algorithm for an adaptive learning system that calculates the total boundary length of a regular star-shaped badge, which has 5 equal sides, where the length of each side adjusts based on student performance level. The system should compute the complete distance around the badge using the current side length value selected by the adaptive difficulty system.
    

    """
import math

def perimeter_pentagon(a):
    """
    Design an algorithm for an adaptive learning system that calculates the total boundary length of a regular star-shaped badge, which has 5 equal sides, where the length of each side adjusts based on student performance level. The system should compute the complete distance around the badge using the current side length value selected by the adaptive difficulty system.
    

    """
    perimeter = 5 * a
    return perimeter