Gary is an architect designing a structure with a piece in the shape of a square prism. The structure has a height of 12
 feet, and the area of the base is 25
 square feet.

What is the total surface area of Gary’s structure?

To find the total surface area of Gary's square prism, we need to calculate both the lateral surface area and the area of the two square bases.

1. **Identify the given values:**
   - Height \( h = 12 \) feet
   - Area of the base \( A_{\text{base}} = 25 \) square feet

2. **Calculate the side length of the base (since it's a square):**
   Since the area of a square base is \( s^2 \), where \( s \) is the side length, we have:
   \[
   s^2 = 25
   \]
   Solving for \( s \), we get:
   \[
   s = \sqrt{25} = 5 \text{ feet}
   \]

3. **Calculate the lateral surface area:**
   The lateral surface area of a prism is given by the perimeter of the base multiplied by the height. The perimeter of the square base is \( 4 \times s = 4 \times 5 = 20 \) feet, so:
   \[
   \text{Lateral Surface Area} = \text{Perimeter} \times h = 20 \times 12 = 240 \text{ square feet}
   \]

4. **Calculate the area of both bases:**
   Since there are two square bases, the total area of the bases is:
   \[
   2 \times A_{\text{base}} = 2 \times 25 = 50 \text{ square feet}
   \]

5. **Calculate the total surface area:**
   Adding the lateral surface area and the area of the bases, we get:
   \[
   \text{Total Surface Area} = 240 + 50 = 290 \text{ square feet}
   \]

### Answer:
The total surface area of Gary’s structure is **290 square feet**.

Would you like more details, or do you have any questions?

#### Related Questions:
1. How would the surface area change if the height were doubled?
2. What would the surface area be if the base area increased to 36 square feet?
3. How does the total surface area formula change for a rectangular prism?
4. How would you find the volume of this structure?
5. What if the base were a different shape, such as a hexagon? How would the calculations differ?

#### Tip:
For prisms, always break down surface area into lateral and base components for clearer calculations.

Gary is an architect designing a structure with a piece in the shape of a square prism. The structure has a height of 12 feet, and the area of the base is 25 square feet. What is the total surface area of Gary’s structure?

Learn how to calculate the total surface area of a square prism with a base area of 25 square feet and a height of 12 feet. This solution includes step-by-step calculations for finding the lateral surface area, base area, and total surface area, suitable for Grades 6-8 students studying geometry and prism properties.

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