To find the shaded area of the figure, let’s analyze and break it down into simpler shapes.

Step-by-Step Solution

1. Calculate the Area of the Entire Rectangle:

   • The dimensions of the rectangle are given as $11 \, \text{m}$ (width) and $9.9 \, \text{m}$ (height).
   • The area of the rectangle $A_{\text{rect}}$ is: $A_{\text{rect}} = 11 \times 9.9 = 108.9 \, \text{m}^2$

2. Calculate the Area of the Triangular Cutout:

   • The triangular cutout has a base of $8.5 \, \text{m}$ and a height of $4.5 \, \text{m}$ (since $9.9 - 5.4 = 4.5$).
   • The area of the triangle $A_{\text{triangle}}$ is: $A_{\text{triangle}} = \frac{1}{2} \times 8.5 \times 4.5 = 19.125 \, \text{m}^2$

3. Calculate the Shaded Area:

   • To find the shaded area, subtract the area of the triangle from the area of the rectangle: $A_{\text{shaded}} = A_{\text{rect}} - A_{\text{triangle}} = 108.9 - 19.125 = 89.775 \, \text{m}^2$

Answer

The shaded area is approximately: $\text{Shaded Area} = 89.775 \, \text{m}^2$

Would you like further details on this solution, or do you have any questions?

Here are 5 related questions to deepen your understanding:

1. How would you calculate the area if the triangle's height or base was different?
2. What if the shape cut out was a semicircle instead of a triangle?
3. How can we find the perimeter of the shaded region?
4. How would this calculation change if the figure was not a right triangle?
5. Can we solve this problem using coordinate geometry?

Tip: When breaking down a shape, always verify each dimension carefully to avoid calculation errors.