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**This shows the net of a square pyramid. What is the surface area of the pyramid?**

This is the net of a square pyramid. To find the surface area of the pyramid, we need to calculate the area of both the square base and the four triangular faces.

### Given:
- The side of the square base is 10 inches.
- The slant height of each triangular face is 15 inches.

### 1. Area of the square base:
The area \( A_{\text{square}} \) of the square base is given by:

\[
A_{\text{square}} = \text{side}^2 = 10^2 = 100 \, \text{in}^2
\]

### 2. Area of the triangular faces:
Each triangular face has a base of 10 inches (equal to the side of the square) and a height (slant height) of 15 inches. The area \( A_{\text{triangle}} \) of one triangular face is:

\[
A_{\text{triangle}} = \frac{1}{2} \times \text{base} \times \text{height} = \frac{1}{2} \times 10 \times 15 = 75 \, \text{in}^2
\]

Since there are 4 triangular faces, the total area of the triangular faces is:

\[
A_{\text{total triangles}} = 4 \times 75 = 300 \, \text{in}^2
\]

### 3. Total surface area:
The total surface area \( A_{\text{total}} \) is the sum of the area of the square base and the area of the four triangular faces:

\[
A_{\text{total}} = A_{\text{square}} + A_{\text{total triangles}} = 100 + 300 = 400 \, \text{in}^2
\]

Thus, the surface area of the pyramid is **400 square inches**.

Would you like more details or further clarifications?

Here are 5 related questions to explore this further:
1. How would the surface area change if the slant height was increased to 20 inches?
2. What is the lateral surface area (excluding the base) of the pyramid?
3. How can you calculate the volume of this pyramid?
4. If the base side length doubled, what would be the new surface area?
5. What if the triangular faces were isosceles triangles instead of equilateral?

**Tip:** When calculating the surface area of a pyramid, remember to calculate both the base area and the lateral faces.

This shows the net of a square pyramid. What is the surface area of the pyramid?

Learn how to calculate the surface area of a square pyramid with a base length of 10 inches and a slant height of 15 inches. The solution uses geometry formulas for the area of a square and the area of a triangle, and is suitable for students in Grades 6-9.

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