Figure $A B C D E F$ has $A B=8, B C=15$, and $E F=5$, as shown. Determine the perimeter of $A B C D E F$.

![](https://cdn.mathpix.com/cropped/2024_04_17_ab5f9723a8aff65a55ebg-2.jpg?height=361&width=504&top_left_y=1023&top_left_x=1187)
The perimeter of $A B C D E F$ equals $A B+B C+C D+D E+E F+F A$.

Since all angles in the diagram are right angles, then $A B$ and $E F$ are parallel to $C D$.

Also, the sum of their lengths equals the length of $C D$.

Similarly, $A F$ and $E D$ are parallel to $B C$ and $A F+E D=B C$.

Therefore, the perimeter is

$$
\begin{aligned}
A B+B C+C D+D E+E F+F A & =(A B+E F+C D)+(B C+E D+A F) \\
& =(A B+E F+(A B+E F))+(B C+B C) \\
& =2(A B+E F)+2(B C) \\
& =2(8+5)+2(15) \\
& =26+30 \\
& =56
\end{aligned}
$$

ANSWER: 56

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