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The image contains a question asking to calculate the total surface area of a pyramid. Here's the key information from the image:

- The pyramid has a square base, with each side of the base measuring **5 cm**.
- The slant height of the pyramid is **12 cm**.

### To calculate the total surface area of the pyramid:
The total surface area (\(A_{total}\)) of a pyramid consists of two parts:
1. **The area of the base** (\(A_{base}\)).
2. **The lateral surface area** (\(A_{lateral}\)).

#### 1. Area of the Base:
The base is a square, so the area of the base is given by:
\[
A_{base} = \text{side}^2 = 5 \, \text{cm} \times 5 \, \text{cm} = 25 \, \text{cm}^2
\]

#### 2. Lateral Surface Area:
The lateral surface area is the sum of the areas of the triangular faces. Each triangle has a base of 5 cm (the side of the square) and a slant height of 12 cm.

The area of one triangular face is:
\[
A_{\text{triangle}} = \frac{1}{2} \times \text{base} \times \text{height} = \frac{1}{2} \times 5 \, \text{cm} \times 12 \, \text{cm} = 30 \, \text{cm}^2
\]

Since there are four triangular faces, the total lateral surface area is:
\[
A_{lateral} = 4 \times 30 \, \text{cm}^2 = 120 \, \text{cm}^2
\]

#### 3. Total Surface Area:
Now, sum the area of the base and the lateral surface area:
\[
A_{total} = A_{base} + A_{lateral} = 25 \, \text{cm}^2 + 120 \, \text{cm}^2 = 145 \, \text{cm}^2
\]

Thus, the total surface area of the pyramid is **145 cm²**.

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Would you like more details or further explanation? Here are 5 related questions to explore:

1. How do you calculate the volume of a pyramid?
2. What is the significance of slant height in pyramids?
3. How does the surface area change if the base becomes a rectangle instead of a square?
4. Can you calculate the height of the pyramid if the slant height is given but the actual height is unknown?
5. How would the formula change for a pyramid with a hexagonal base?

**Tip:** Remember, for any pyramid, the slant height is not the same as the vertical height. The slant height is measured along the face of the pyramid.

Calculate the total surface area of a pyramid with a square base, each side of the base measuring 5 cm, and a slant height of 12 cm.

Learn how to calculate the total surface area of a pyramid with a square base. This geometry problem includes key concepts such as the surface area of a square and triangular faces, as well as the use of slant height to determine lateral surface area. Suitable for students in Grades 7-9, the example uses a 5 cm square base and 12 cm slant height.

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