hello
to solve this question, let's add up all the areas from the sides given and equate it to the total area of the prism. Then we can also denote the side with the missing area as x
[tex]\begin{gathered} 396=42+72+42+72+x+x \\ 396=228+2x \\ 2x=396-228 \\ 2x=168 \\ \text{divide both sides by the coefficient of x} \\ \frac{2x}{2}=\frac{168}{2} \\ x=84 \end{gathered}[/tex]
now we have established the area of the missing sides as 84cm^2
but then from careful observation, the figure with the missing side have a shape of a rectangle and we can use the formula of area of a rectangle to find the missing side.
[tex]\begin{gathered} a=l\times w \\ a=84\operatorname{cm}^2 \\ l=? \\ w=7\operatorname{cm} \\ 84=l\times7 \\ 84=7l \\ \frac{84}{7}=\frac{7l}{7} \\ l=12\operatorname{cm} \end{gathered}[/tex]
from the calculations above, the missing side is equal to 12cm
