We are given the dimensions of several rectangular prisms and either the surface area or one dimension is missing. We are asked to find the missing values.

1. Problem Description

We are given the dimensions of several rectangular prisms and either the surface area or one dimension is missing. We are asked to find the missing values.

2. Solution Steps

Let $l, w, h$ denote the length, width, and height of a rectangular prism.

The surface area $SA$ of a rectangular prism is given by the formula:

$SA = 2(lw + lh + wh)$

First Rectangular Prism:

Given: $l=6, w=2, h=9$

$SA = 2(6*2 + 6*9 + 2*9) = 2(12 + 54 + 18) = 2(84) = 168$.

Second Rectangular Prism:

Given: $SA = 24, w=5, h=5$

$24 = 2(l*5 + l*5 + 5*5)$

$12 = 5l + 5l + 25$

$12 = 10l + 25$

$10l = -13$

$l = -1.3$. Since dimensions cannot be negative, there must be an error in the problem statement. The surface area associated with the rectangular prism with dimensions 6, 2, and 9 seems to be missing.

Third Rectangular Prism:

Given: $l=16, w=5, h=2$

$SA = 2(16*5 + 16*2 + 5*2) = 2(80 + 32 + 10) = 2(122) = 244$.

Fourth Rectangular Prism:

Given: $SA = 136, l=16, w=5$

$136 = 2(16*5 + 16*h + 5*h)$

$68 = 80 + 16h + 5h$

$68 = 80 + 21h$

$21h = -12$

$h = -12/21 = -4/7$. Since dimensions cannot be negative, there must be an error in the problem statement.

Fifth Rectangular Prism:

Given: $l=5, w=5, h=7$

$SA = 2(5*5 + 5*7 + 5*7) = 2(25 + 35 + 35) = 2(95) = 190$.

Sixth Rectangular Prism:

Given: $l=12, w=12, h=9$

$SA = 2(12*12 + 12*9 + 12*9) = 2(144 + 108 + 108) = 2(360) = 720$.

3. Final Answer

First Rectangular Prism: 168

Second Rectangular Prism: Calculation error

Third Rectangular Prism: 244

Fourth Rectangular Prism: Calculation error

Fifth Rectangular Prism: 190

Sixth Rectangular Prism: 720