To find the surface area of the triangular pyramid, we need to calculate the area of all its triangular faces and sum them up.

Given Information:

1. Base Triangle Dimensions:

   • Each side of the base triangle is $9 \, \text{m}$.
   • The height of the base triangle is not given explicitly, so we'll calculate it using the formula for the height of an equilateral triangle.

   $\text{Height} = \frac{\sqrt{3}}{2} \cdot \text{side length} = \frac{\sqrt{3}}{2} \cdot 9 = 7.8 \, \text{m}.$

   Area of the base triangle: $\text{Area} = \frac{1}{2} \cdot \text{base} \cdot \text{height} = \frac{1}{2} \cdot 9 \cdot 7.8 = 35.1 \, \text{m}^2.$

2. Three Lateral Triangles:

   • Each lateral triangle has a base of $9 \, \text{m}$ and height of $6 \, \text{m}$ (as indicated in the image).
   • Area of each lateral triangle: $\text{Area} = \frac{1}{2} \cdot \text{base} \cdot \text{height} = \frac{1}{2} \cdot 9 \cdot 6 = 27 \, \text{m}^2.$
   • Total area of the three lateral triangles: $3 \cdot 27 = 81 \, \text{m}^2.$

Total Surface Area:

$\text{Total Surface Area} = \text{Base Area} + \text{Lateral Areas} = 35.1 + 81 = 116.1 \, \text{m}^2.$

Final Answer:

$\boxed{116.1 \, \text{square meters}}$

Do you want additional details or have any questions? Here are some follow-up topics:

1. How to derive the formula for the height of an equilateral triangle.
2. Why the lateral faces are considered congruent.
3. How to calculate the surface area of pyramids with different base shapes.
4. How to compute the volume of this pyramid.
5. How scaling the dimensions affects the surface area.

Tip: Always check if the base is equilateral or irregular before proceeding with calculations.