To solve for the area of the shaded region, let's break the problem down step by step:

Step 1: Calculate the area of the larger rectangle

The larger rectangle has dimensions of 7 cm (length) by 5 cm (height).

$\text{Area of the rectangle} = \text{length} \times \text{height} = 7 \, \text{cm} \times 5 \, \text{cm} = 35 \, \text{cm}^2$

Step 2: Calculate the area of the triangle (shaded region)

The shaded region is a triangle with a base of 4 cm and a height of 3 cm.

$\text{Area of the triangle} = \frac{1}{2} \times \text{base} \times \text{height} = \frac{1}{2} \times 4 \, \text{cm} \times 3 \, \text{cm} = 6 \, \text{cm}^2$

Step 3: The final area of the shaded region

The area of the shaded region (triangle) is simply the result we calculated in Step 2:

$\text{Area of the shaded region} = 6 \, \text{cm}^2$

The area of the shaded region is $6 \, \text{cm}^2$.

Would you like further clarification on any part of this, or additional details? Here are some related questions to expand your understanding:

1. How is the formula for the area of a triangle derived?
2. What other methods can be used to calculate the area of irregular shapes?
3. How can you verify if a triangle is a right triangle using its dimensions?
4. How does the Pythagorean theorem relate to triangles and areas?
5. What is the difference between finding the perimeter and area of geometric shapes?

Tip: When working with composite shapes, break them down into basic shapes like rectangles and triangles for easier calculations.