To find the area of the shaded part on the right, we can break it down into simpler geometric shapes and calculate each area separately before adding them together. Here’s the breakdown based on the image:

1. Identify the shapes and dimensions:

   • The shaded area appears to be a combination of a larger trapezoid and a smaller rectangle cut out from it.

2. Calculate the area of the larger trapezoid:

   • The trapezoid has parallel sides of 10 m (top) and 8 m (bottom), with a height of 7 m.
   • The area of a trapezoid is given by: $\text{Area} = \frac{1}{2} \times (\text{Base}_1 + \text{Base}_2) \times \text{Height}$
   • Plugging in the values: $\text{Area}_{\text{trapezoid}} = \frac{1}{2} \times (10 + 8) \times 7 = \frac{1}{2} \times 18 \times 7 = 63 \, \text{m}^2$

3. Calculate the area of the rectangle to subtract:

   • The rectangle has a width of 5 m and a height of 5 m.
   • The area of a rectangle is given by: $\text{Area} = \text{Width} \times \text{Height}$
   • Plugging in the values: $\text{Area}_{\text{rectangle}} = 5 \times 5 = 25 \, \text{m}^2$

4. Subtract the area of the rectangle from the trapezoid: $\text{Area}_{\text{shaded}} = \text{Area}_{\text{trapezoid}} - \text{Area}_{\text{rectangle}} = 63 - 25 = 38 \, \text{m}^2$

Final Answer

The area of the shaded part is $38 \, \text{m}^2$.

Would you like further details on any step?

Here are some related questions you might find interesting:

1. How would the area calculation change if the dimensions of the cut-out rectangle were different?
2. What is the perimeter of the shaded region?
3. How would you calculate the area if the shaded region was irregular without distinct shapes?
4. Can the area of the shaded region be calculated using integration if it had curved edges?
5. How would this area calculation change if the shaded part were rotated?

Tip: When calculating areas of complex shapes, try breaking them into simple geometric figures to make calculations easier.