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Let's break down the problem step by step:

### Total Area of the Lot:
The rectangular lot has dimensions of 12 cm (length) and 6 cm (width).
\[
\text{Total Area} = 12 \, \text{cm} \times 6 \, \text{cm} = 72 \, \text{cm}^2
\]

### Area of the Shapes Inside:

1. **Rectangular Area for Stalls (6 cm by 4 cm)**:
\[
\text{Area of Rectangle} = 6 \, \text{cm} \times 4 \, \text{cm} = 24 \, \text{cm}^2
\]

2. **Triangular Area for the Food Zone**:
The base and height of the triangle are both 4 cm, since it's right-angled.
\[
\text{Area of Triangle} = \frac{1}{2} \times 4 \, \text{cm} \times 4 \, \text{cm} = 8 \, \text{cm}^2
\]

3. **Square Area for the Stage**:
The side length of the square is 2 cm.
\[
\text{Area of Square} = 2 \, \text{cm} \times 2 \, \text{cm} = 4 \, \text{cm}^2
\]

### Total Occupied Area:
\[
\text{Total Occupied Area} = 24 \, \text{cm}^2 + 8 \, \text{cm}^2 + 4 \, \text{cm}^2 = 36 \, \text{cm}^2
\]

### Vacant Area:
\[
\text{Vacant Area} = \text{Total Area} - \text{Total Occupied Area} = 72 \, \text{cm}^2 - 36 \, \text{cm}^2 = 36 \, \text{cm}^2
\]

Thus, the area that will be left vacant is **36 cm²**, which corresponds to option **C**.

Would you like further details, or do you have any other questions?

Here are some related questions for further practice:
1. How do you calculate the area of a right-angled triangle with different dimensions?
2. What would be the total area if the rectangle for stalls was doubled in size?
3. If the square stage was moved to a different spot, would the vacant area change?
4. How would you calculate the area of more complex shapes like trapezoids or circles?
5. How does the formula for the area of a triangle relate to the formula for a rectangle?

**Tip**: When calculating areas, always check if the shapes are simple (like squares, rectangles, and triangles) to apply basic geometric formulas.

En un lote de terreno rectangular se planea la realización de la feria navideña del pueblo. Internamente se distribuyen tres áreas: una rectangular, una triangular y una cuadrada. ¿Cuál es el área del terreno que se dejará vacío?

This problem involves calculating the area of a rectangular lot that includes internal rectangular, triangular, and square areas. Learn how to find the vacant space by subtracting the areas of the internal shapes from the total area. Suitable for students in Grades 5-7.

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