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The image provided shows a three-dimensional geometric figure, specifically a square pyramid. The problem asks for the surface area of the pyramid, and the dimensions are as follows:

- **Base side length**: 10 yards
- **Slant height**: 12 yards
- **Height of the triangular face**: 8 yards (although this value is less relevant to surface area calculation)

### Steps to Calculate the Surface Area

1. **Calculate the Area of the Base:**
   Since the base is a square:
   \[
   \text{Area of the base} = \text{side}^2 = 10^2 = 100 \text{ square yards}
   \]

2. **Calculate the Area of the Triangular Faces:**
   Each triangular face has a base equal to the side length of the square (10 yards) and a height equal to the slant height (12 yards). The area of one triangular face is:
   \[
   \text{Area of one triangular face} = \frac{1}{2} \times \text{base} \times \text{height} = \frac{1}{2} \times 10 \times 12 = 60 \text{ square yards}
   \]
   Since there are 4 triangular faces, the total area of the triangular faces is:
   \[
   \text{Total area of the triangular faces} = 4 \times 60 = 240 \text{ square yards}
   \]

3. **Add the Areas Together:**
   The total surface area of the pyramid is the sum of the area of the base and the total area of the triangular faces:
   \[
   \text{Total Surface Area} = 100 + 240 = 340 \text{ square yards}
   \]

### Final Answer:
The surface area of the pyramid is **340 square yards**.

Would you like more details or have any questions?

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Here are five related questions that might deepen your understanding:

1. How would the surface area change if the side length of the square base was doubled?
2. What would be the surface area if the pyramid had a rectangular base instead of a square one?
3. How would you calculate the volume of this pyramid?
4. If the slant height was increased by 5 yards, what would be the new surface area?
5. How does the height of the triangular faces relate to the slant height in surface area calculations?

**Tip:** Remember that the slant height is crucial in calculating the area of the triangular faces of a pyramid. Always ensure you use the correct height for accurate surface area calculations.

Calculate the surface area of a square pyramid with a base side length of 10 yards and a slant height of 12 yards. This problem explores key geometric concepts, including the surface area of pyramids. Suitable for students in Grades 8-10.

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