To calculate the area of the shaded part of the shape, we can approach the problem by finding the area of the outer trapezoid and subtracting the area of the inner rectangle.

Step-by-Step Solution

1. Calculate the Area of the Outer Trapezoid

   The area $A$ of a trapezoid is given by: $A = \frac{1}{2} \times (a + b) \times h$ where:

   • $a$ and $b$ are the lengths of the two parallel sides,
   • $h$ is the height (perpendicular distance between the parallel sides).

   In this case:

   • The lengths of the two parallel sides are $5 \text{ cm}$ (top) and $12 \text{ cm}$ (bottom).
   • The height is $8 \text{ cm}$.

   Substituting these values: $A_{\text{trapezoid}} = \frac{1}{2} \times (5 + 12) \times 8 = \frac{1}{2} \times 17 \times 8 = 68 \text{ cm}^2$

2. Calculate the Area of the Inner Rectangle

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

   Here, the rectangle has:

   • Length = $5 \text{ cm}$,
   • Width = $3 \text{ cm}$.

   So: $A_{\text{rectangle}} = 5 \times 3 = 15 \text{ cm}^2$

3. Calculate the Shaded Area

   The shaded area is the area of the trapezoid minus the area of the rectangle: $A_{\text{shaded}} = A_{\text{trapezoid}} - A_{\text{rectangle}}$ $A_{\text{shaded}} = 68 - 15 = 53 \text{ cm}^2$

Final Answer

The area of the shaded part of the shape is: $\boxed{53 \text{ cm}^2}$

Would you like more details on any step or have additional questions?

Here are some related questions for further practice:

1. How would you calculate the area of the trapezoid if only the diagonals were given?
2. What would be the area if the inner shape were a triangle instead of a rectangle?
3. How can the perimeter of the shaded area be calculated?
4. What is the difference between the formula for a trapezoid and a parallelogram?
5. If the dimensions of the inner rectangle were doubled, how would that affect the shaded area?

Tip: When working with composite shapes, separate the shapes, calculate their areas individually, and then combine or subtract them as needed.