Question: wall thickness is $6\text{mm}$ on top+$6\text{mm}$ bottom and $12 \text{mm}$ on sides
1. **Problem Statement:**
We are given a wall thickness of $6\text{mm}$ on the top and bottom, and $12\text{mm}$ on the sides.
2. **Understanding the Problem:**
The wall thickness varies: $6\text{mm}$ vertically (top and bottom) and $12\text{mm}$ horizontally (sides).
3. **Application:**
This information is typically used to calculate the internal dimensions of a structure if the external dimensions are known, or vice versa.
4. **Formula:**
If $L_{ext}$ and $W_{ext}$ are the external length and width, and $t_{top} = t_{bottom} = 6\text{mm}$, $t_{side} = 12\text{mm}$, then the internal dimensions are:
$$L_{int} = L_{ext} - 2 \times 6 = L_{ext} - 12$$
$$W_{int} = W_{ext} - 2 \times 12 = W_{ext} - 24$$
5. **Explanation:**
Subtract twice the thickness on each side because thickness applies to both sides (top and bottom or left and right).
6. **Example:**
If external length is $100\text{mm}$ and external width is $80\text{mm}$:
$$L_{int} = 100 - 12 = 88\text{mm}$$
$$W_{int} = 80 - 24 = 56\text{mm}$$
This gives the internal dimensions accounting for the wall thickness.