Area of a Regular Pentagram | Python3 implementation of the approach ; Function to return the area of triangle BCD ; Using Golden ratio ; Calculate area of triangle BCD ; Return area of all 5 triangles are the same ; Function to return the area of regular pentagon ; Calculate the area of regular pentagon using above formula ; Return area of regular pentagon ; Function to return the area of pentagram ; Area of a pentagram is equal to the area of regular pentagon and five times the area of Triangle ; Driver code
import math NEW_LINE PI = 3.14159 NEW_LINE def areaOfTriangle ( d ) : NEW_LINE INDENT c = 1.618 * d NEW_LINE s = ( d + c + c ) / 2 NEW_LINE area = math . sqrt ( s * ( s - c ) * ( s - c ) * ( s - d ) ) NEW_LINE return 5 * area NEW_LINE DEDENT def areaOfRegPentagon ( d ) : NEW_LINE INDENT global PI NEW_LINE cal = 4 * math . tan ( PI / 5 ) NEW_LINE area = ( 5 * d * d ) / cal NEW_LINE return area NEW_LINE DEDENT def areaOfPentagram ( d ) : NEW_LINE INDENT return areaOfRegPentagon ( d ) + areaOfTriangle ( d ) NEW_LINE DEDENT d = 5 NEW_LINE print ( areaOfPentagram ( d ) ) NEW_LINE