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The problem asks for an expression representing the total amount of timber used to frame a square embroidery piece with side length \( a \) cm, where the timber has a width of 4 cm.

### Solution:

1. The embroidery piece has a side length of \( a \) cm.
2. The timber adds 4 cm to each side, so the total side length including the timber will be:
   \[
   a + 2 \times 4 = a + 8 \text{ cm}
   \]
   This accounts for 4 cm on each side.

3. The total timber used forms the perimeter of the larger square (embroidery + timber). The perimeter of a square is given by \( 4 \times \text{side length} \).

   The side length of the entire square (including the timber) is \( a + 8 \) cm, so the total perimeter is:
   \[
   4 \times (a + 8) = 4a + 32 \text{ cm}
   \]

### Final Expression:
The total amount of timber used is \( 4a + 32 \) cm.

Would you like more details or have any questions about this?

Here are 5 related questions to expand on this concept:
1. What would happen to the total timber if the timber width were doubled?
2. How does the total amount of timber change if the side length of the embroidery piece changes?
3. Can you find the total area covered by the embroidery and the timber?
4. How would you calculate the amount of timber used if the timber had a different width on each side?
5. What if the embroidery piece had a rectangular shape instead of a square?

**Tip:** The perimeter of a square is always 4 times its side length. This can simplify many geometric problems involving squares.

A square piece of embroidery has side length a cm and is framed by timber of width 4 cm. Write an expression for the total amount of timber used in cm.

Learn how to write an expression for the total timber used to frame a square embroidery piece with side length a cm and timber width of 4 cm. This problem explores the concept of perimeter and introduces algebraic expression formation, suitable for students in Grades 6-8.

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