[tex]\begin{gathered} a)198in^{2} \\ b)3 \\ c)x=6 \end{gathered}[/tex]
1) We can see here the net surface of that gingerbread house, so we need to find the area of the 4 triangles and the rectangle. So we can write out:
a)
[tex]\begin{gathered} A_{\Delta}=\frac{b\cdot h}{2} \\ 2A_{\Delta}=2(\frac{b\cdot h}{2})=2(\frac{6\cdot8}{2})=48in^{2} \\ A_R=12\cdot8=96in^{2} \\ 2A_{\Delta}=2(\frac{4.5\cdot12}{2})=54in^{2} \\ A_H=54+96+48 \\ A_H=198in^{2} \end{gathered}[/tex]
Note that not all triangles are congruent to each other, so we needed to do it separately.
b) We can find the number of batches by setting a direct proportion:
[tex]\begin{gathered} 1----50in^{2} \\ x----198in^{2} \\ x=\frac{198}{50}=3.96 \end{gathered}[/tex]
We can count batches with whole numbers and despite 3.96 is almost 4 we can tell that the answer is 3 batches
c) Since Wendy wants a Gingerbread house twice as much, and we can see rectangles we can write out the following equation:
[tex]\begin{gathered} (12\cdot7)+(12\cdot7)+12x+12x+7x+7x=2\cdot198 \\ 12\cdot\: 7+12\cdot\: 7+12x+12x+7x+7x=2\cdot\: 198 \\ 12\cdot\: 7+12\cdot\: 7+38x=2\cdot\: 198 \\ 2\cdot\: 12\cdot\: 7+38x=2\cdot\: 198 \\ 168+38x=2\cdot\: 198 \\ 168+38x=396 \\ 168+38x-168=396-168 \\ 38x=228 \\ \frac{38x}{38}=\frac{228}{38} \\ x=6 \end{gathered}[/tex]
And that is the missing side.
