To find the missing dimension of the rectangular prism, we can use the formula for the surface area of a rectangular prism, which is given by:
\[ \text{Surface Area} = 2(lw + lh + wh) \]
where \( l \), \( w \), and \( h \) are the length, width, and height of the prism, respectively.
Given:
- Surface Area = 208 cm²
- Two dimensions are \( l = 2 \) cm and \( w = 10 \) cm.
Let \( h \) be the height we need to find.
Now, we can substitute these values into the surface area formula:
\[ 208 = 2(2 \cdot 10 + 2 \cdot h + 10 \cdot h) \]
First, calculate \( 2 \cdot 10 \):
\[ 208 = 2(20 + 2h + 10h) \] \[ 208 = 2(20 + 12h) \]
Next, divide both sides by 2:
\[ 104 = 20 + 12h \]
Now, subtract 20 from both sides:
\[ 84 = 12h \]
Finally, divide by 12 to solve for \( h \):
\[ h = \frac{84}{12} = 7 \]
Thus, the missing dimension \( h \) is:
\[ \text{Height} = 7 \text{ cm} \]