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Let's break down the problem:

You have a rectangle with dimensions 6 cm by 7 cm, and a right triangle has been cut out of it to form the shaded region. The dimensions of the triangle are 3 cm for both the base and the height.

### Step-by-step Solution:

1. **Area of the original rectangle:**
   The area \( A_{\text{rectangle}} \) of a rectangle is calculated using the formula:
   \[
   A_{\text{rectangle}} = \text{base} \times \text{height} = 6 \, \text{cm} \times 7 \, \text{cm} = 42 \, \text{cm}^2
   \]

2. **Area of the right triangle cut out:**
   The area \( A_{\text{triangle}} \) of a right triangle is calculated using the formula:
   \[
   A_{\text{triangle}} = \frac{1}{2} \times \text{base} \times \text{height} = \frac{1}{2} \times 3 \, \text{cm} \times 3 \, \text{cm} = 4.5 \, \text{cm}^2
   \]

3. **Area of the shaded region:**
   The shaded region is the area of the rectangle minus the area of the right triangle:
   \[
   A_{\text{shaded}} = A_{\text{rectangle}} - A_{\text{triangle}} = 42 \, \text{cm}^2 - 4.5 \, \text{cm}^2 = 37.5 \, \text{cm}^2
   \]

Thus, the area of the shaded region is **37.5 cm²**.

Would you like further details or have any questions?

### Related Questions:
1. How do you calculate the perimeter of the remaining shaded shape?
2. What would the area be if the base of the rectangle were increased by 2 cm?
3. If the triangle were equilateral instead of a right triangle, how would you calculate its area?
4. How would you find the area of the shaded region if multiple triangles were cut out?
5. How do you generalize the formula for finding the shaded area in any shape?

### Tip:
When calculating the area of a composite figure, always subtract the areas of the cut-out shapes from the total area of the original figure.

Se corta un triángulo rectángulo de un rectángulo para crear la región sombreada que se muestra a continuación. Calcular el área de esta región. Incluir las unidades correctas en la respuesta.

Learn how to calculate the area of a shaded region formed by cutting a right triangle out of a rectangle. This problem involves geometry concepts such as the area of rectangles and right triangles. Suitable for students in Grades 6-8.

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