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In the diagram, the terrace is depicted with the following dimensions: 

- \( BC = 19.5 \) meters
- \( AB = 9.2 \) meters
- \( DE = 26.5 \) meters
- \( AD = 6.8 \) meters

From the image, the terrace can be divided into a rectangle \(ABCD\) and a right triangle \(ADE\).

1. **Rectangle \(ABCD\)**:
   - Area = length \( \times \) width = \(AB \times BC\) = \(9.2 \, \text{m} \times 19.5 \, \text{m}\) = \(179.4 \, \text{m}^2\).

2. **Right Triangle \(ADE\)**:
   - The base \(AD\) = \(6.8 \, \text{m}\)
   - The height, which is the difference between \(DE\) and \(BC\) = \(26.5 \, \text{m} - 19.5 \, \text{m} = 7 \, \text{m}\)
   - Area = \(\frac{1}{2} \times \text{base} \times \text{height}\) = \(\frac{1}{2} \times 6.8 \, \text{m} \times 7 \, \text{m}\) = \(23.8 \, \text{m}^2\).

Thus, the total area of the terrace = Area of \(ABCD\) + Area of \(ADE\) = \(179.4 \, \text{m}^2 + 23.8 \, \text{m}^2 = 203.2 \, \text{m}^2\).

The most practical way to calculate the area of the terrace, based on the options given, is to:
- **Separate the surface into a rectangle and a triangle, find the area of each, and sum them.**

This option directly applies to the shape and dimensions given, providing a straightforward method to obtain the total area. Would you like more details or have any further questions about this calculation?

Here are some related questions you might consider:
1. How does the area calculation change if new dimensions are provided?
2. What would be the perimeter of the entire terrace?
3. How could this shape be rearranged to maximize or minimize the area?
4. What would be the impact of altering the height of triangle \(ADE\) on the total area?
5. How would you calculate the area if the terrace had additional triangular or rectangular sections?

**Tip:** Always double-check that the dimensions of combined shapes match at their boundaries to avoid miscalculations in area.

Un arquitecto decide construir una terraza en un edificio con la forma y dimensiones que aparecen en la siguiente figura: La forma más práctica de calcular el área de la terraza es: ¿Multiplicar las longitudes de la base y la altura de cada una de las figuras y sumarlas? ¿Separar la superficie en un rectángulo y un triángulo, luego encontrar el área de cada uno y sumarlas? ¿Sumar la longitud de cada uno de los lados de la terraza? ¿Dividir la figura en triángulos congruentes, hallar el área de uno de ellos y multiplicarla por el número de triángulos resultantes?

Learn how to calculate the area of a terrace composed of a rectangle and a right triangle. The problem uses basic geometry formulas such as area of a rectangle (length × width) and area of a right triangle (1/2 × base × height) to find the total area. This tutorial is suitable for students in Grades 8-10.

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