https://file.aiquickdraw.com/mathbot/file/1737121557969qfmm1d4k.jpg

The polygon in the image appears to have a symmetrical and complex shape, with straight segments and protruding triangular sections. Let’s break it into simpler components to calculate the area:

### Steps to Calculate the Area:
1. **Divide the Shape into Sections**:
   - A large central rectangle with dimensions \( 20 \, \text{cm} \times 5 \, \text{cm} \).
   - Two identical triangular sections protruding on the top and bottom, each with a base of \( 5 \, \text{cm} \) and height of \( 2.5 \, \text{cm} \), located on the left.
   - Two identical triangular sections on the right side, each also with a base of \( 5 \, \text{cm} \) and height of \( 2.5 \, \text{cm} \).

2. **Calculate Individual Areas**:
   - Area of the central rectangle:
     \[
     \text{Area} = \text{Length} \times \text{Width} = 20 \, \text{cm} \times 5 \, \text{cm} = 100 \, \text{cm}^2
     \]
   - Area of one triangle (on the left or right):
     \[
     \text{Area} = \frac{1}{2} \times \text{Base} \times \text{Height} = \frac{1}{2} \times 5 \, \text{cm} \times 2.5 \, \text{cm} = 6.25 \, \text{cm}^2
     \]
   - Total area for the four triangles:
     \[
     4 \times 6.25 \, \text{cm}^2 = 25 \, \text{cm}^2
     \]

3. **Add the Areas**:
   Combine the areas of the central rectangle and the four triangles:
   \[
   \text{Total Area} = 100 \, \text{cm}^2 + 25 \, \text{cm}^2 = 125 \, \text{cm}^2
   \]

### Final Answer:
The area of the polygon is:
\[
\boxed{125 \, \text{cm}^2}
\]

Would you like a detailed breakdown of each calculation or further clarifications? 

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### Related Questions:
1. What is the perimeter of this polygon?
2. How would the area change if the central rectangle's width increased by \( 2 \, \text{cm} \)?
3. How do you calculate the area of irregular polygons in general?
4. How can symmetry help simplify area calculations in complex shapes?
5. Can you derive a formula to calculate the area of a polygon with similar protrusions?

### Tip:
When dealing with irregular shapes, always divide the shape into basic geometric figures (rectangles, triangles, circles) to simplify area calculations.

Learn how to calculate the area of a complex polygon by dividing it into a rectangle and triangles. The problem includes the use of key geometry formulas and step-by-step solutions. Suitable for Grades 6-8.

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