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The image you uploaded shows a square pyramid, both in a 3D view and as a net. The pyramid has a square base with side lengths of 10 units, and its slant height (the height of the triangular faces) is 12 units.

To calculate the surface area of the pyramid, we need to:

1. **Surface Area of the Base (Square)**:
   The base is a square with side length 10 units. The area \( A_{\text{base}} \) of a square is given by:
   \[
   A_{\text{base}} = \text{side}^2 = 10^2 = 100 \text{ square units}
   \]

2. **Surface Area of the Triangular Faces**:
   Each triangular face has a base of 10 units (the side length of the square) and a height of 12 units (the slant height of the pyramid). The area \( A_{\text{triangle}} \) of a triangle is given by:
   \[
   A_{\text{triangle}} = \frac{1}{2} \times \text{base} \times \text{height} = \frac{1}{2} \times 10 \times 12 = 60 \text{ square units}
   \]
   Since there are 4 triangular faces, the total surface area of the triangles is:
   \[
   4 \times A_{\text{triangle}} = 4 \times 60 = 240 \text{ square units}
   \]

3. **Total Surface Area**:
   The total surface area \( A_{\text{total}} \) is the sum of the area of the base and the area of the 4 triangular faces:
   \[
   A_{\text{total}} = A_{\text{base}} + 4 \times A_{\text{triangle}} = 100 + 240 = 340 \text{ square units}
   \]

Thus, the total surface area of the pyramid is **340 square units**.

Would you like further details or have any questions?

Here are some related questions:
1. How would the surface area change if the side length of the base was doubled?
2. What is the lateral surface area (excluding the base) of this pyramid?
3. How would you calculate the volume of this pyramid?
4. What is the slant height’s relation to the height of the pyramid?
5. Can you calculate the area of just one triangular face if the base length changes?

**Tip**: Always remember that for pyramids, the slant height is crucial for calculating the surface area of the triangular faces.

Use the polyhedron to label all the lengths in this net. Then calculate the surface area.

Learn how to calculate the surface area of a square pyramid with a slant height of 12 units and base side length of 10 units. Explore key geometry concepts and surface area calculations through this problem, perfect for Grades 6-8.

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