Problem 7 · The perimeter of the staircase polygon
Projecting the sides: the perimeter equals a rectangle's.
Integer answer, at most 4 digitsThe figure shows a polygon with all right angles, and some measurements are given. What is the perimeter of the polygon?
Copa Cangur · SCM
Medium
Closed answer
Reasoned solution
Key idea: in a right-angled “staircase” polygon like this one, projecting all sides onto the axes shows that the rightward segments add up to the same as the leftward ones (the total width), and the upward segments the same as the downward ones (the total height).
The total height is the right side: $12$ cm. The total width: the interior $10$ cm segment and the bottom $8$ cm segment complement each other exactly (the middle step starts where the $10$ cm segment ends): $10 + 8 = 18$ cm.
$$P = 2\,(18 + 12) = 60\ \text{cm}.$$
Answer: 60