https://file.aiquickdraw.com/mathbot/file/1726854204434zxoxeyoa.jpg

The image depicts an irregular polygon for which the area needs to be calculated. Given the dimensions:

- \( a = 8 \, \text{cm} \)
- \( b = 6 \, \text{cm} \)
- \( c = 4 \, \text{cm} \)

This shape can be broken down into three rectangles:

1. **Top rectangle** with dimensions \( a \times c \).
2. **Middle rectangle** with dimensions \( b \times c \).
3. **Bottom rectangle** with dimensions \( a \times c \).

The total area \( A \) of the polygon is the sum of the areas of these three rectangles:

\[
A = 2 \cdot (a \times c) + (b \times c)
\]

Now, substituting the given values:

\[
A = 2 \cdot (8 \, \text{cm} \times 4 \, \text{cm}) + (6 \, \text{cm} \times 4 \, \text{cm})
\]

Let me calculate the result.The area of the polygon is \( 88 \, \text{cm}^2 \).

Would you like more details or have any questions?

Here are five related questions to further explore this topic:
1. How can we calculate the perimeter of this polygon?
2. What is the difference between finding the area of a regular versus an irregular polygon?
3. How does breaking down complex shapes into rectangles help in geometry?
4. How would the area change if one of the dimensions \( a \), \( b \), or \( c \) were doubled?
5. Can you think of a method to calculate the area of more complex polygons?

**Tip:** When dealing with irregular shapes, it's often useful to decompose them into simpler geometric figures like rectangles or triangles.

Berechnen Sie den Flächeninhalt des Vielecks, wenn a = 8 cm, b = 6 cm und c = 4 cm lang ist.

Lernen Sie, wie Sie den Flächeninhalt eines Vielecks berechnen, wenn a = 8 cm, b = 6 cm und c = 4 cm sind. Dieser Ansatz verwendet die Zerlegung der Figur in Rechtecke, um die Gesamtfläche zu bestimmen.

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