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The problem in the image asks to calculate the area of the red shaded region within a rectangle and to write down the solution process. Here is the step-by-step solution:

### Given:
- The rectangle has dimensions 20 cm by 10 cm.
- The red shaded region is a right triangle formed by diagonals intersecting.

### Steps:

1. **Identify the Key Components:**
   - The rectangle has a width of 20 cm and a height of 10 cm.
   - The triangle in the red shaded region is formed by one of the diagonals of the rectangle, and another diagonal divides the rectangle.

2. **Calculate the Area of the Rectangle:**
   \[
   \text{Area of the rectangle} = \text{width} \times \text{height} = 20 \, \text{cm} \times 10 \, \text{cm} = 200 \, \text{cm}^2
   \]

3. **Area of the Triangle (Red Shaded Region):**
   The red shaded area is a right triangle. The base and height of this triangle correspond to the segments of the rectangle’s width and height, which are 8 cm and 10 cm respectively.
   \[
   \text{Area of the triangle} = \frac{1}{2} \times \text{base} \times \text{height} = \frac{1}{2} \times 8 \, \text{cm} \times 10 \, \text{cm} = 40 \, \text{cm}^2
   \]

### Final Answer:
- The area of the red shaded region is **40 cm²**.

Would you like further details or explanations on any part? Here are some related questions to consider:

1. How would you find the area of the other triangle formed by the diagonals?
2. What is the total area of the two triangles formed by the diagonals?
3. How can you calculate the perimeter of the red shaded triangle?
4. What would the area be if the base were 12 cm instead of 8 cm?
5. How does the area of the red triangle compare to the total area of the rectangle?
6. Can you find the lengths of the diagonals using the Pythagorean theorem?
7. How would you calculate the area of the triangle if the rectangle were not a right angle?
8. What is the relationship between the areas of the triangles formed by the diagonals?

**Tip:** When dealing with areas, it's always a good practice to verify by considering different approaches, like using geometric properties or algebraic formulas.

Learn how to calculate the area of the red shaded triangle within a rectangle with a detailed step-by-step solution. This problem covers key geometric concepts, including the area of a rectangle and the area of a right triangle. Suitable for students in Grades 7-9.

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