What is the perimeter of the rectilinear shape shown in figure (4) below? The shape is composed of several rectangles.

The given side lengths are:

• Left outer vertical side: $24\text{m}$
• Bottom left horizontal side: $15\text{m}$
• Inner left vertical side (of the cut-out): $8\text{m}$
• Inner horizontal side (top of the cut-out): $6\text{m}$
• Inner right vertical side (of the cut-out): $8\text{m}$
• Bottom right horizontal side: $15\text{m}$

This is a rectilinear polygon, meaning all its angles are right angles.

• The total width of the shape is the sum of the bottom horizontal segments and the inner horizontal segment:

$$\text{Total width} = 15\text{m} + 6\text{m} + 15\text{m} = 36\text{m}$$

This total width corresponds to the length of the top outer horizontal side.

• The total height of the shape on the right side must be equal to the total height on the left side:

$$\text{Right outer vertical side} = 24\text{m}$$

The perimeter is the sum of all the segments identified:

$$\text{Perimeter} = 24\text{m} + 15\text{m} + 8\text{m} + 6\text{m} + 8\text{m} + 15\text{m} + 24\text{m} + 36\text{m}$$ $$\text{Perimeter} = (24 + 15 + 8 + 6 + 8 + 15 + 24 + 36)\text{m}$$ $$\text{Perimeter} = (39 + 8 + 6 + 8 + 15 + 24 + 36)\text{m}$$ $$\text{Perimeter} = (47 + 6 + 8 + 15 + 24 + 36)\text{m}$$ $$\text{Perimeter} = (53 + 8 + 15 + 24 + 36)\text{m}$$ $$\text{Perimeter} = (61 + 15 + 24 + 36)\text{m}$$ $$\text{Perimeter} = (76 + 24 + 36)\text{m}$$ $$\text{Perimeter} = (100 + 36)\text{m}$$ $$\text{Perimeter} = 136\text{m}$$

The perimeter of shape (4) is $\boxed{\text{136m}}$.