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To calculate the surface area of the pyramid, we need to find the area of its base and the areas of the four triangular faces.

The given pyramid is a square pyramid, as indicated by the base being a square with sides of 16 feet.

1. **Area of the base**:
   \[
   \text{Area of base} = 16 \times 16 = 256 \text{ square feet}
   \]

2. **Area of the triangular faces**:
   We need to find the slant height of the triangular faces. The given height of the pyramid is 15 feet. Using the Pythagorean theorem, we can find the slant height (\(l\)).

   The slant height is the hypotenuse of a right triangle where one leg is half of the base (\(8\) feet) and the other leg is the height of the pyramid (\(15\) feet).

   \[
   l = \sqrt{15^2 + 8^2} = \sqrt{225 + 64} = \sqrt{289} = 17 \text{ feet}
   \]

   Each triangular face has a base of 16 feet and a height (slant height) of 17 feet.

   \[
   \text{Area of one triangular face} = \frac{1}{2} \times \text{base} \times \text{height} = \frac{1}{2} \times 16 \times 17 = 136 \text{ square feet}
   \]

   Since there are four triangular faces:
   \[
   \text{Total area of the triangular faces} = 4 \times 136 = 544 \text{ square feet}
   \]

3. **Total surface area of the pyramid**:
   \[
   \text{Total surface area} = \text{Area of base} + \text{Total area of triangular faces} = 256 + 544 = 800 \text{ square feet}
   \]

The surface area of the pyramid is \(800\) square feet.

Would you like more details on any specific part of this calculation? 

Here are some additional questions you might have:
1. How to find the volume of the pyramid?
2. What is the lateral surface area of the pyramid?
3. How to derive the slant height using different methods?
4. How to calculate the area of a different shape base pyramid?
5. How to find the height if the slant height and base side are given?

**Tip:** Always double-check your calculations for each step to ensure accuracy in geometry problems.

Learn how to calculate the surface area of a square pyramid with a base side of 16 feet and a height of 15 feet. This problem involves finding the area of the base square and the triangular faces using the Pythagorean theorem to determine the slant height. Suitable for students in Grades 7-9.

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