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We are given a right triangle \(ABC\) where:

- \(DF \perp AC\)
- \(DE \perp BC\)
- \(DF = 2 \, \text{cm}\)
- \(DE = 1 \, \text{cm}\)
- \(AC = 6 \, \text{cm}\)
- \(BC = 4 \, \text{cm}\)

To find the area of triangle \(ABC\), we will use the formula for the area of a triangle:

\[
\text{Area} = \frac{1}{2} \times \text{base} \times \text{height}
\]

In this case, triangle \(ABC\) is a right triangle, so we can take \(BC\) as the base and \(AC\) as the height. Thus, the area is:

\[
\text{Area of } \triangle ABC = \frac{1}{2} \times BC \times AC = \frac{1}{2} \times 4 \times 6 = 12 \, \text{cm}^2
\]

It seems that the problem may involve subtracting smaller areas (like the areas of triangles \(DEF\), etc.), but the full instructions are not clear on that.

However, based on the provided formula, the area of triangle \(ABC\) is 12 cm², but the choices suggest that the result might be derived differently.

Would you like me to verify the smaller triangles' areas or clarify further details? Let me know!

Yukarıdaki verilere göre, Alan(ABC) kaç cm² dir?

This problem involves calculating the area of triangle ABC given its base and height. It covers key concepts of triangle geometry and uses the basic area formula for a right triangle. The provided dimensions are AC = 6 cm and BC = 4 cm.

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