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To calculate the surface area of the frustum, we need to address two components: the lateral (side) surface area and the areas of the top and bottom square faces.

### 1. **Base Areas**:
- The **bottom face** of the frustum is a square with a side length of 48 mm, so its area is:
  \[
  A_{\text{bottom}} = 48^2 = 2304 \text{ mm}^2
  \]
  
- The **top face** is a square with a side length of 37 mm, so its area is:
  \[
  A_{\text{top}} = 37^2 = 1369 \text{ mm}^2
  \]

### 2. **Lateral Surface Area** (Trapezoidal Faces):
Each lateral face is a trapezium (trapezoid), and we will compute the area of one trapezoidal face and multiply by 4 (since there are four lateral faces).

For one trapezium, the parallel sides are the heights of the top and bottom squares:  
- Larger base: \( 48 \) mm  
- Smaller base: \( 37 \) mm  
The **slant height** of each trapezoid face is given as 37 mm.

The area of a trapezium is:
\[
A_{\text{trapezium}} = \frac{1}{2} \times (b_1 + b_2) \times h
\]
Where:
- \( b_1 = 48 \) mm (larger base),
- \( b_2 = 37 \) mm (smaller base),
- \( h = 37 \) mm (slant height).

Now, calculate the area:
\[
A_{\text{trapezium}} = \frac{1}{2} \times (48 + 37) \times 37 = \frac{1}{2} \times 85 \times 37 = 1572.5 \text{ mm}^2
\]

Since there are four trapezoidal faces, the total lateral surface area is:
\[
A_{\text{lateral}} = 4 \times 1572.5 = 6290 \text{ mm}^2
\]

### 3. **Total Surface Area**:
The total surface area of the frustum is the sum of the top, bottom, and lateral surface areas:
\[
A_{\text{total}} = A_{\text{top}} + A_{\text{bottom}} + A_{\text{lateral}} = 1369 + 2304 + 6290 = 9963 \text{ mm}^2
\]

Rounding to 1 decimal place, the surface area of the frustum is:
\[
A_{\text{total}} \approx 9963.0 \text{ mm}^2
\]

Would you like more details or clarifications? Here are some additional questions for you:

1. What is the formula for the volume of a frustum?
2. How does the surface area of a frustum change if the slant height increases?
3. Can we calculate the volume of this frustum with the given data?
4. What is the relationship between a pyramid and its frustum?
5. How would the surface area formula differ for a frustum of a cone?

**Tip:** Always check the unit consistency when working with area and volume problems.

A frustum is formed by removing a small square-based pyramid from a similar, larger one. Work out the surface area of the frustum.

Learn how to calculate the surface area of a frustum formed by removing a smaller square-based pyramid from a larger one. This geometry problem includes the area of trapezoidal lateral faces and square top and bottom faces. Suitable for students in Grades 9-12.

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