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This image depicts three squares arranged around a right triangle, likely applying the Pythagorean theorem to find the area of the shaded square.

In this setup:
- The two smaller squares have areas of \( 34 \, \text{cm}^2 \) and \( 47 \, \text{cm}^2 \).
- According to the Pythagorean theorem: \( c^2 = a^2 + b^2 \), where \( c^2 \) is the area of the largest square (shaded) and \( a^2 \) and \( b^2 \) are the areas of the other two squares.

Thus, the area of the shaded square is:
\[
\text{Area of shaded square} = 34 \, \text{cm}^2 + 47 \, \text{cm}^2 = 81 \, \text{cm}^2
\]

Hence, the area of the shaded square is \( 81 \, \text{cm}^2 \).

Would you like a detailed breakdown or have any other questions?

Here are 5 related questions:
1. How does the Pythagorean theorem apply to real-life geometry problems?
2. Can you use this method to find the side lengths of the squares?
3. What other geometric shapes could this principle apply to?
4. How would the areas change if the dimensions of the smaller squares were different?
5. Can this method be applied to non-right triangles?

**Tip**: In geometry, it's often helpful to draw out relationships between areas and side lengths to spot patterns more easily.

This problem demonstrates how to apply the Pythagorean theorem to find the area of a shaded square. By summing the areas of two smaller squares (34 cm² and 47 cm²), the total area of the shaded square is calculated as 81 cm². Suitable for students in Grades 7-9.

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