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?

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.