To find how many times larger the surface area of prism B is compared to prism A, we first need to calculate the surface area of each prism.
The formula for the surface area \( SA \) of a rectangular prism is given by:
\[ SA = 2(lw + lh + wh) \]
For prism A:
- Dimensions: \( l = 2 \), \( w = 4 \), \( h = 6 \)
Calculating the surface area:
\[ SA_A = 2(2 \cdot 4 + 2 \cdot 6 + 4 \cdot 6) \]
Calculating each term:
\[ = 2(8 + 12 + 24) = 2(44) = 88 \]
So, the surface area of prism A is \( 88 \) square units.
For prism B:
- Dimensions: \( l = 6 \), \( w = 12 \), \( h = 18 \)
Calculating the surface area:
\[ SA_B = 2(6 \cdot 12 + 6 \cdot 18 + 12 \cdot 18) \]
Calculating each term:
\[ = 2(72 + 108 + 216) = 2(396) = 792 \]
So, the surface area of prism B is \( 792 \) square units.
Now, to find how many times larger the surface area of prism B is compared to prism A:
\[ \text{Times larger} = \frac{SA_B}{SA_A} = \frac{792}{88} = 9 \]
Thus, the surface area of prism B is 9 times larger than the surface area of prism A.