To solve for the total surface area of this prism, we need to find the area of each face and sum them. This prism has two triangular faces and three rectangular faces. Let's go through each one step-by-step.

Step 1: Find the Area of the Triangular Faces

Each triangle has:

• A base of $12$ ft.
• A height of $8$ ft (indicated in the diagram).

The area of a triangle is given by: $\text{Area of triangle} = \frac{1}{2} \times \text{base} \times \text{height}$ So, for each triangular face: $\text{Area} = \frac{1}{2} \times 12 \times 8 = 48 \, \text{ft}^2$ Since there are two triangular faces: $\text{Total area of triangles} = 2 \times 48 = 96 \, \text{ft}^2$

Step 2: Find the Area of the Rectangular Faces

There are three rectangular faces, each with the following dimensions:

1. $12 \, \text{ft} \times 18 \, \text{ft}$
2. $10 \, \text{ft} \times 18 \, \text{ft}$
3. $10 \, \text{ft} \times 18 \, \text{ft}$ (same as the previous one)

Calculating each rectangular area:

1. $12 \times 18 = 216 \, \text{ft}^2$
2. $10 \times 18 = 180 \, \text{ft}^2$
3. $10 \times 18 = 180 \, \text{ft}^2$

Adding these: $\text{Total area of rectangles} = 216 + 180 + 180 = 576 \, \text{ft}^2$

Step 3: Add the Areas Together

$\text{Total Surface Area} = \text{Area of triangles} + \text{Area of rectangles}$ $\text{Total Surface Area} = 96 + 576 = 672 \, \text{ft}^2$

Final Answer

The total surface area of the prism is: $\boxed{672 \, \text{ft}^2}$

Thus, the correct answer is (B) 672 ft².

Would you like more details, or have any questions about the solution?

Here are some related questions to expand your understanding:

1. How would you find the surface area if the prism had a different triangular base?
2. How does changing the height of the triangle affect the total surface area?
3. What is the volume of this prism?
4. How do you calculate the lateral surface area of a prism?
5. What if the prism's rectangular faces had different lengths?

Tip: To solve surface area problems for prisms, break down the shape into individual faces, calculate each area, and sum them.