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Obtener el área sombreada A en función de x. A 10

To find the shaded area \( A \) in terms of \( x \), let's analyze the geometry of the figure.

### Description of the Figure:
- The figure is a square with a side length of \( 10 \) units.
- A right triangle is formed inside the square by drawing a diagonal line from one vertex to a point on the opposite side. The triangle has a height of \( 10 \) units and a base of \( x \) units.

### Step-by-Step Calculation:

1. **Area of the Square**:
   - The area of the square is \( \text{Area of square} = 10 \times 10 = 100 \) square units.

2. **Area of the Triangle**:
   - The area of the right triangle inside the square is given by:
   \[
   \text{Area of triangle} = \frac{1}{2} \times \text{base} \times \text{height} = \frac{1}{2} \times x \times 10 = 5x
   \]
   square units.

3. **Shaded Area \( A \)**:
   - The shaded area is the area of the square minus the area of the triangle:
   \[
   A = \text{Area of square} - \text{Area of triangle} = 100 - 5x
   \]

### Final Expression:
The shaded area \( A \) as a function of \( x \) is:
\[
A(x) = 100 - 5x
\]

Would you like further clarification or details on this calculation? Here are some related questions:

1. What is the maximum value of \( x \) for which the shaded area is still positive?
2. How does the area change as \( x \) increases?
3. What is the significance of the coefficient \( -5 \) in the expression \( A(x) = 100 - 5x \)?
4. How would the expression change if the square had a different side length?
5. What happens to the shaded area if \( x = 0 \) or \( x = 10 \)?

**Tip**: When dealing with composite areas like this, it's helpful to subtract the area of the unwanted region from the total area to get the desired result.

Aprende cómo encontrar el área sombreada A en función de x en este problema de geometría. Este problema implica el cálculo de áreas de un cuadrado y un triángulo rectángulo dentro de él. Adecuado para estudiantes de secundaria.

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