The given shape is a composite figure consisting of a rectangular prism with a semicylinder attached to one of its faces. To calculate the surface area, we need to find the areas of each component and sum them up.

Step-by-step breakdown:

1. Surface area of the rectangular part:

   • The rectangular part has 5 rectangular faces, as one face is replaced by the semicylinder.
   • Dimensions of the rectangular part:
     • Length = 6.5 m
     • Height = 1.4 m
     • Width = 5 m

   The surface area of a rectangle is calculated by $A = \text{length} \times \text{width}$.

   • Front and back faces: 2 rectangles with dimensions $6.5 \times 1.4$.
     • $A_{\text{front/back}} = 2 \times (6.5 \times 1.4) = 18.2 \, \text{m}^2$.
   • Top and bottom faces: 2 rectangles with dimensions $6.5 \times 5$.
     • $A_{\text{top/bottom}} = 2 \times (6.5 \times 5) = 65 \, \text{m}^2$.
   • One side face (the remaining rectangular face opposite to the semicylinder) has dimensions $5 \times 1.4$.
     • $A_{\text{side}} = 5 \times 1.4 = 7 \, \text{m}^2$.

   Total area of the rectangular part: $A_{\text{rectangular}} = 18.2 + 65 + 7 = 90.2 \, \text{m}^2.$

2. Surface area of the semicylinder:

   • The curved surface area of a cylinder is given by $A = \pi r h$, where $r$ is the radius and $h$ is the height (or length) of the cylinder.
   • The radius $r = \frac{5}{2} = 2.5 \, \text{m}$, and the height $h = 6.5 \, \text{m}$. $A_{\text{curved}} = \pi \times 2.5 \times 6.5 = 51.06 \, \text{m}^2.$
   • The semicircle base area at the end is $A = \frac{1}{2} \times \pi r^2$. $A_{\text{semicircle}} = \frac{1}{2} \times \pi \times (2.5)^2 = 9.82 \, \text{m}^2.$ Since there is only one semicircle base, we do not multiply it by 2.

   Total area of the semicylinder part: $A_{\text{semicylinder}} = 51.06 + 9.82 = 60.88 \, \text{m}^2.$

Total surface area of the composite figure:

$A_{\text{total}} = A_{\text{rectangular}} + A_{\text{semicylinder}} = 90.2 + 60.88 = 151.08 \, \text{m}^2.$

Thus, the total surface area of the shape is approximately 151.08 m².

Would you like further details or clarifications on any part of the solution?

Related questions:

1. How would the surface area change if the length of the rectangular part increased?
2. What is the volume of this composite shape?
3. How would you calculate the surface area if the shape had a full cylinder instead of a semicylinder?
4. How would the surface area formula change if the shape were scaled by a factor of 2?
5. Can you calculate the perimeter of the semicircular face?

Tip:

When working with composite shapes, always break them down into simpler components to calculate surface area or volume more easily.