But How Much Was Removed?

Relevant wiki: Length and Area

Let the other 4 sides be denoted as $a,b,c$ and $d$ as shown above.

Since we are given that the shape is rectilinear, then the side lengths $a$ and $b$ are parallel to each other, and their sum $a+b$ is equal to the bottom side length of the figure, $10\text{ cm}$ .

Similarly, the side lengths $c$ and $d$ are parallel to each other, and their sum $c+d$ is equal to the left length of the left side length of the figure, $15\text{ cm}$ .

Hence, the perimeter of the composite figure is

$15\text{ cm} + 10\text{ cm} + (a+b) + (c+d) = 15\text{ cm} + 10\text{ cm} + 10\text{ cm} + 15\text{ cm} = \boxed{50}\text{ cm}$