The problem requires us to find the area of the shaded region, which is formed by removing a rectangle from a right triangle.

Step 1: Find the area of the right triangle.

The formula for the area of a triangle is: $\text{Area of Triangle} = \frac{1}{2} \times \text{base} \times \text{height}$

• Base = 6 m
• Height = 4 m

$\text{Area of Triangle} = \frac{1}{2} \times 6 \times 4 = 12 \, \text{m}^2$

Step 2: Find the area of the rectangle.

The area of a rectangle is given by: $\text{Area of Rectangle} = \text{length} \times \text{width}$

• Length = 2 m
• Width = 3 m

$\text{Area of Rectangle} = 2 \times 3 = 6 \, \text{m}^2$

Step 3: Calculate the area of the shaded region.

The shaded region is the area of the triangle minus the area of the rectangle: $\text{Area of Shaded Region} = \text{Area of Triangle} - \text{Area of Rectangle} = 12 - 6 = 6 \, \text{m}^2$

Final Answer:

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

Would you like further details or clarifications? Here are some related questions:

1. What would happen if the rectangle dimensions changed?
2. How do you calculate the area of other polygons?
3. What is the significance of using the correct units in geometry problems?
4. How do you find the perimeter of the shaded region in this problem?
5. Can this problem be solved using coordinate geometry?

Tip: Always ensure that units are consistent throughout the calculation to avoid mistakes!