IKMC 2007 - Grades 5-6 - Self-study Question 15

The squares are formed by intersecting the segment $AB$ of 24 cm by the broken line $AA_1A_2\ldots A_{12}B$ (see the figure). Find the length of $AA_1A_2\ldots A_{12}B$.

Source recovery: the compilation and official Pakistan PDF omit the figure. The matching original figure below is from Austrian Benjamin 2007, Q17; labels and the 24 cm statement match.