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Shown is a diagram of a square based pyramid. What is the surface area of this pyramid in square centimetre?

To find the surface area of the square-based pyramid, we need to calculate the area of its base and the area of its four triangular sides.

### Given:
1. **Base side length (s)**: 6 cm
2. **Slant height of the pyramid (l)**: 5 cm

### Step-by-step Solution:

1. **Area of the Base:**
   The base is a square, so the area of the base (A_base) is:
   \[
   A_{\text{base}} = s^2 = 6 \times 6 = 36 \, \text{cm}^2
   \]

2. **Area of the Triangular Sides:**
   Each of the four triangular sides has a base equal to the side of the square (6 cm) and a slant height of 5 cm.

   The area of one triangular side (A_triangle) is:
   \[
   A_{\text{triangle}} = \frac{1}{2} \times \text{base} \times \text{slant height} = \frac{1}{2} \times 6 \times 5 = 15 \, \text{cm}^2
   \]

   Since there are four triangular sides, the total area of the triangles (A_triangles_total) is:
   \[
   A_{\text{triangles total}} = 4 \times 15 = 60 \, \text{cm}^2
   \]

3. **Total Surface Area:**
   The total surface area of the pyramid (A_total) is the sum of the area of the base and the total area of the triangular sides:
   \[
   A_{\text{total}} = A_{\text{base}} + A_{\text{triangles total}} = 36 + 60 = 96 \, \text{cm}^2
   \]

### Final Answer:
The surface area of the square-based pyramid is **96 square centimeters**.

Would you like further details, or do you have any questions?

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Here are some related questions you might find interesting:
1. How would the surface area change if the slant height were increased to 7 cm?
2. What would the surface area be if the base side length were doubled?
3. How do you find the volume of a square-based pyramid?
4. What is the difference between the slant height and the perpendicular height of a pyramid?
5. How does the surface area formula change for a pyramid with a rectangular base?

**Tip:** To find the surface area of any pyramid, always calculate the base area and add it to the total area of all its triangular sides.

Shown is a diagram of a square based pyramid. What is the surface area of this pyramid in square centimetres?

Learn how to find the surface area of a square-based pyramid with a base side length of 6 cm and a slant height of 5 cm. This problem covers key geometric concepts, including the surface area of a pyramid and the formulas involved. Suitable for students in Grades 8-10.

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