[tex]Area_{total}=181\text{ square inches}[/tex]
Explanation
Step 1
to find the total area of a rectangular prism , do
[tex]\text{Area}_{rec\tan gular\text{ prism}}=2(length\cdot width+widht\cdot height+length\cdot heigth)[/tex]
then, for prism 1
let
length=4 in
widht=1 in
height=3 in
so, the area is
[tex]\begin{gathered} \text{Area}_{rec\tan gular\text{ prism}1}=2(length\cdot width+widht\cdot height+length\cdot heigth) \\ \text{Area}_{rec\tan gular\text{ prism}1}=2(4\cdot1+1\cdot3+4\cdot3) \\ \text{Area}_{rec\tan gular\text{ prism}1}=2(4+3+12) \\ \text{Area}_{rec\tan gular\text{ prism}1}=2(19) \\ \text{Area}_{rec\tan gular\text{ prism}1}=38in^2 \end{gathered}[/tex]
Step 2
now, for prism2 ( the bigger)
Let
length07
width=3
heigth=5
replace to find the area
[tex]\begin{gathered} \text{Area}_{rec\tan gular\text{ prism}}=2(length\cdot width+widht\cdot height+length\cdot heigth) \\ \text{Area}_{rec\tan gular\text{ prism}}=2(7\cdot3+3\cdot5+7\cdot5) \\ \text{Area}_{rec\tan gular\text{ prism}}=2(21+15+35) \\ \text{Area}_{rec\tan gular\text{ prism}}=2(71) \\ \text{Area}_{rec\tan gular\text{ prism}}=142 \end{gathered}[/tex]
Step 3
finally, add the areas to find the total
[tex]\begin{gathered} Area_{total}=Area_1+Area_2 \\ Area_{total}=38In^2+143in^2 \\ Area_{total}=181\text{ square inches} \end{gathered}[/tex]
I hope this helps you
