To solve for the surface area of the given shape, we need to recognize the figure. The image appears to represent a quadrilateral with diagonals intersecting inside the figure.

Steps to calculate the surface area:

1. Divide the figure into two triangles by using the diagonal that connects the 5 m and 6 m sides.
2. We'll calculate the area of these two triangles separately and then sum them up.

For the first triangle (on the left):

• It is a right triangle with legs 4 m and 5 m.
• Use the formula for the area of a triangle:
  $\text{Area} = \frac{1}{2} \times \text{base} \times \text{height}$ $\text{Area} = \frac{1}{2} \times 4 \times 5 = 10 \text{ square meters}$

For the second triangle (on the right):

• This triangle has sides 6 m and 5 m, and we can assume it also uses the diagonal as its height. So, the base is 5 m and the height is 5 m.
• The area is: $\text{Area} = \frac{1}{2} \times 6 \times 5 = 15 \text{ square meters}$

Total surface area:

$\text{Total Area} = 10 + 15 = 25 \text{ square meters}$

Thus, the surface area of the given figure is 25 square meters.

Would you like further clarification on any of these steps?

Here are five related questions to extend your understanding:

1. How do we calculate the surface area of irregular polygons?
2. What would change in the surface area if the diagonal had a different length?
3. How can the Pythagorean theorem help verify dimensions in right triangles?
4. What other formulas are useful for finding areas of polygons?
5. Can the concept of dividing complex shapes into simpler ones be applied to 3D figures?

Tip: Always double-check the units in surface area problems to ensure correct final answers.