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find the perimeter of these shapes. Assume all angles are right angles.

To find the perimeter of the shape, we'll add up the lengths of all the sides. 

The shape consists of a rectangle at the bottom and some steps or indents at the top. Here's how we can break it down:

1. **Bottom side:** 20 cm (given).
2. **Left vertical side:** 15 cm (given).
3. **Right vertical side:** 15 cm (given).
4. **Top horizontal sections:** These can be divided into five sections as follows:
   - The first and last segments are outside segments: Let's assume these segments are each \( x \) cm long.
   - There are three inner segments with their lengths, which are indentations or "steps" of the same size.

   Since the total width is 20 cm and we have five segments, the sum of these segments' lengths equals 20 cm. 
   
   Given that the shape appears symmetric, assume the middle segments are equal:
   - The total width of the middle three segments \( 3y \) equals the remaining distance.
   
   \( 2x + 3y = 20 \, \text{cm} \)

5. **Vertical segments:** There are additional vertical segments contributing to the perimeter:
   - If each indentation or "step" has a height \( z \), then each vertical segment in the steps contributes to the perimeter.

We can now summarize the perimeter based on the identified components:

\[ \text{Perimeter} = 20 \, \text{cm} + 15 \, \text{cm} + 15 \, \text{cm} + 20 \, \text{cm} \text{ (top horizontal and vertical parts summed up)} \]

Given the symmetry and pattern of segments, we proceed as follows:

\[
\text{Perimeter} = 2 \times 20 \, \text{cm} + 2 \times 15 \, \text{cm} + \text{Top and Vertical sections}
\]

Let's assume each segment is 4 cm, as the total width divided by 5 gives this:
- 2 segments from top
- 3 segments from vertical sides, each segment size contributes to 3 parts.

Thus, summing the entire structure’s perimeter gives:
\[ P = 20 + 15 + 20 + 15 = 70 \, \text{cm} \]

Now for an estimation of perimeter sum:

Top + Verticals \( =  4 \times 10 + 3 \times 5 = 40 + 15 = 55 \).

Finally, we add them all:

Total perimeter \[ P = 20 + 20 + 30 = 140 \, \text{cm}. \]

The approximate perimeter is **140 cm**.

Would you like to go into further details or have any specific questions? Here are some related questions:

1. How would the perimeter change if the shape was scaled up by a factor of 2?
2. What would be the area of this shape?
3. Can you determine the length of each segment if additional dimensions were provided?
4. How does symmetry play a role in simplifying the calculation of the perimeter?
5. If the shape were rotated, would the perimeter change?

**Tip:** Always check for symmetry and patterns in geometrical shapes, as they can simplify complex perimeter and area calculations.

Learn how to calculate the perimeter of a shape with right angles using a detailed step-by-step solution. This problem involves identifying side lengths, symmetry considerations, and adding up all contributing segments. Suitable for students in Grades 5-7.

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