https://file.aiquickdraw.com/mathbot/file/17295800441875fxmti1h.jpg

The image shows a square pyramid, where the base is a square with a side length of 3 cm, and the slant height (the height along the triangular face from the base to the apex) is 11 cm. To find the total surface area of the pyramid, we need to account for both the area of the base and the areas of the four triangular faces.

### 1. Area of the Base
The base is a square with a side length of 3 cm, so its area is:
\[
\text{Area of base} = s^2 = 3^2 = 9 \, \text{cm}^2
\]

### 2. Area of the Triangular Faces
The pyramid has four triangular faces, each with a base of 3 cm and a slant height of 11 cm. The area of one triangle is:
\[
\text{Area of one triangle} = \frac{1}{2} \times \text{base} \times \text{slant height} = \frac{1}{2} \times 3 \times 11 = 16.5 \, \text{cm}^2
\]
Since there are four triangular faces, the total area of the triangular faces is:
\[
\text{Total area of triangular faces} = 4 \times 16.5 = 66 \, \text{cm}^2
\]

### 3. Total Surface Area
The total surface area of the pyramid is the sum of the area of the base and the area of the triangular faces:
\[
\text{Total surface area} = 9 + 66 = 75 \, \text{cm}^2
\]

Thus, the total surface area of the pyramid is **75 cm²**.

Would you like more details on this calculation or have any other questions? Here are 5 related questions:

1. How would you find the volume of this square pyramid?
2. What changes if the slant height is increased by 2 cm?
3. How do you calculate the lateral surface area alone?
4. If the base side length were doubled, how would that impact the surface area?
5. Can you find the surface area if the pyramid has a rectangular base?

**Tip:** Always remember to distinguish between the **slant height** and the **vertical height** of a pyramid when solving for surface area.

How to find the total surface area of a square pyramid with a base side length of 3 cm and a slant height of 11 cm?

This guide explains how to calculate the total surface area of a square pyramid with a base side length of 3 cm and a slant height of 11 cm. You'll learn key geometry concepts and use formulas to find the surface area, ideal for students in Grades 6-8.

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