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.

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.