https://file.aiquickdraw.com/mathbot/file/1727368453847h126u9p8.jpg

The image shows the net of a square pyramid. To find the surface area, we need to calculate the area of the square base and the area of the four triangular faces.

1. **Base Area** (square):
   - The base is a square with a side length of 40 cm.
   - Area of square = side² = \( 40^2 = 1600 \, \text{cm}^2 \).

2. **Triangular Faces Area**:
   - There are 4 triangular faces, and the base of each triangle is also 40 cm.
   - The height of each triangle (slant height) is 20 cm.
   - Area of one triangle = \( \frac{1}{2} \times \text{base} \times \text{height} \).
   - So, area of one triangle = \( \frac{1}{2} \times 40 \times 20 = 400 \, \text{cm}^2 \).
   - Total area of four triangles = \( 4 \times 400 = 1600 \, \text{cm}^2 \).

3. **Total Surface Area**:
   - Surface area = base area + area of four triangles.
   - Surface area = \( 1600 + 1600 = 3200 \, \text{cm}^2 \).

Thus, the surface area of the square pyramid is **3200 cm²**.

Would you like more details or have any questions?

Here are 5 related questions:
1. How would the surface area change if the slant height was increased?
2. What is the difference between lateral surface area and total surface area of a pyramid?
3. Can you derive the formula for the surface area of a general pyramid?
4. How does the surface area formula change for pyramids with rectangular bases?
5. How would you calculate the volume of the pyramid in the image?

**Tip:** For 3D shapes like pyramids, always break down the surface into individual faces to calculate the total area easily!

The net of a square pyramid is shown. What is the surface area of the figure?

Learn how to calculate the surface area of a square pyramid with a base of 40 cm and a slant height of 20 cm. This geometry problem breaks down the area of the square base and triangular faces. Suitable for Grades 7-10.

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