1. **State the problem:** We are given a rectangular prism with a square front face of side length 6 cm.
2. **Identify the dimensions:** The front face is a square with sides 6 cm each, so the area of the front face is $6 \times 6 = 36$ cm$^2$.
3. **Given information:** The total surface area is 216 cm$^2$.
4. **Find the missing dimension:** Let the depth (length) of the prism be $x$ cm.
5. **Surface area formula for a rectangular prism:**
$$\text{Surface Area} = 2(lw + lh + wh)$$
where $l$, $w$, and $h$ are the length, width, and height.
6. **Apply the formula:** Since the front face is a square, let $l = h = 6$ cm and $w = x$ cm.
$$216 = 2(6 \times 6 + 6 \times x + 6 \times x)$$
7. **Simplify inside the parentheses:**
$$216 = 2(36 + 6x + 6x) = 2(36 + 12x)$$
8. **Distribute the 2:**
$$216 = 72 + 24x$$
9. **Isolate $x$:**
$$216 - 72 = 24x$$
$$144 = 24x$$
10. **Divide both sides by 24:**
$$\cancel{24}x = \frac{144}{\cancel{24}}$$
$$x = 6$$
11. **Conclusion:** The depth of the prism is 6 cm.
12. **Final answer:** The prism is a cube with side length 6 cm, and the surface area is 216 cm$^2$ as given.
**Answer:** $6.0$ cm (to the nearest tenth)
Rectangular Prism 55268E
Step-by-step solutions with LaTeX - clean, fast, and student-friendly.