To find the area of the shaded region, we can break down the shape into simpler geometric components and sum or subtract their areas accordingly.

Steps to Solve:

1. Identify the Components: The shaded area appears to be a composite shape. The overall outline includes a large trapezoid on the left, with a rectangular cut-out at the top right.

2. Calculate the Area of the Large Trapezoid:

   • The trapezoid has a top base of 10 m, a bottom base of 8 m, and a height of 5 m.
   • The formula for the area of a trapezoid is: $\text{Area of trapezoid} = \frac{1}{2} \times (\text{Base}_1 + \text{Base}_2) \times \text{Height}$
   • Substituting the values: $\text{Area of trapezoid} = \frac{1}{2} \times (10 + 8) \times 5 = \frac{1}{2} \times 18 \times 5 = 45 \text{ m}^2$

3. Calculate the Area of the Cut-Out Rectangle:

   • The cut-out rectangle has dimensions 5 m by 5 m.
   • The area of a rectangle is: $\text{Area of rectangle} = \text{Length} \times \text{Width}$
   • Substituting the values: $\text{Area of rectangle} = 5 \times 5 = 25 \text{ m}^2$

4. Determine the Shaded Area:

   • Subtract the area of the rectangle from the area of the trapezoid to get the area of the shaded region. $\text{Shaded area} = \text{Area of trapezoid} - \text{Area of rectangle} = 45 - 25 = 20 \text{ m}^2$

Answer:

The area of the shaded part is $20 \, \text{m}^2$.

Would you like a deeper explanation or have any questions?

Here are some related questions for further exploration:

1. How would the area change if the dimensions of the cut-out rectangle were different?
2. What is the perimeter of the shaded region?
3. How can you determine the area of irregular shapes in general?
4. How would the formula change if the shape was a parallelogram instead of a trapezoid?
5. Can you determine the centroid (center of mass) of the shaded area?

Tip: When breaking down complex shapes, it’s often helpful to sketch out and label each segment with dimensions before calculating.