To find the surface area of the triangular prism, we'll break it down into its components. The surface area of a prism is the sum of the areas of all its faces, which include the two triangular bases and three rectangular lateral faces.

Step-by-step process:

1. Area of the triangular bases:

   • The triangle has a base of 18 yd and a height of 24 yd.
   • The area of a triangle is given by: $A = \frac{1}{2} \times \text{base} \times \text{height}$ Substituting the values: $A_{\text{triangle}} = \frac{1}{2} \times 18 \, \text{yd} \times 24 \, \text{yd} = 216 \, \text{yd}^2$ Since there are two triangular bases, their total area is: $2 \times 216 = 432 \, \text{yd}^2$

2. Area of the three rectangular faces:

   • The three rectangles are formed by the sides of the triangle (18 yd, 24 yd, and 30 yd) and the prism's length (26 yd).

   For each rectangular face:

   • Rectangle 1 (with side 18 yd and length 26 yd): $A_1 = 18 \, \text{yd} \times 26 \, \text{yd} = 468 \, \text{yd}^2$
   • Rectangle 2 (with side 24 yd and length 26 yd): $A_2 = 24 \, \text{yd} \times 26 \, \text{yd} = 624 \, \text{yd}^2$
   • Rectangle 3 (with side 30 yd and length 26 yd): $A_3 = 30 \, \text{yd} \times 26 \, \text{yd} = 780 \, \text{yd}^2$

   Adding the areas of the three rectangles: $A_{\text{rectangles}} = 468 + 624 + 780 = 1872 \, \text{yd}^2$

3. Total surface area: The total surface area of the prism is the sum of the areas of the two triangular bases and the three rectangular faces: $A_{\text{total}} = 432 \, \text{yd}^2 + 1872 \, \text{yd}^2 = 2304 \, \text{yd}^2$

Thus, the total surface area of the triangular prism is 2304 yd².

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

Here are some related questions to explore:

1. How is the surface area of a rectangular prism different from that of a triangular prism?
2. What is the volume of this triangular prism?
3. How do you calculate the lateral surface area of a prism?
4. How does the surface area change if the length of the prism increases?
5. What are the applications of surface area calculations in real life?

Tip: Always ensure that all units are consistent before performing area calculations.