Answer:
AE = 26 cm and AG = 32.5 cm
Step-by-step explanation:
Given
AB = 12 cm
BD = 12 cm
FD = 6 cm
AC = 12 cm
AD = AB + BD = [tex]12+12=24 \ cm[/tex]
Also segment BC is parallel segment ED which is parallel to segment GF
Now by midpoint theorem we can say that
[tex]\frac{AB}{BD}=\frac{AC}{EC}\\\frac{12}{12}=\frac{13}{EC}\\1 =\frac{13}{EC}\\EC= 13\ cm[/tex]
Now AE = AC + EC = [tex]13+13=26\ cm[/tex]
Also
[tex]\frac{AD}{FD}=\frac{AE}{EG}[/tex]
[tex]\frac{24}{6}=\frac{26}{EG}\\4=\frac{26}{EG}\\EG=\frac{26}{4}\\EG=6.5\ cm[/tex]
Now AG = AE + EG = [tex]26+6.5=32.5\ cm[/tex]
