Question

pedro is charged of covering the display box shown in felt including the bottom what is the the total area

Answer 1

$Area_{total}=181\text{ square inches}$

Explanation

Step 1

to find the total area of a rectangular prism , do

$\text{Area}_{rec\tan gular\text{ prism}}=2(length\cdot width+widht\cdot height+length\cdot heigth)$

then, for prism 1

let

length=4 in

widht=1 in

height=3 in

so, the area is

$\begin{gathered} \text{Area}_{rec\tan gular\text{ prism}1}=2(length\cdot width+widht\cdot height+length\cdot heigth) \\ \text{Area}_{rec\tan gular\text{ prism}1}=2(4\cdot1+1\cdot3+4\cdot3) \\ \text{Area}_{rec\tan gular\text{ prism}1}=2(4+3+12) \\ \text{Area}_{rec\tan gular\text{ prism}1}=2(19) \\ \text{Area}_{rec\tan gular\text{ prism}1}=38in^2 \end{gathered}$

Step 2

now, for prism2 ( the bigger)

Let

length07

width=3

heigth=5

replace to find the area

$\begin{gathered} \text{Area}_{rec\tan gular\text{ prism}}=2(length\cdot width+widht\cdot height+length\cdot heigth) \\ \text{Area}_{rec\tan gular\text{ prism}}=2(7\cdot3+3\cdot5+7\cdot5) \\ \text{Area}_{rec\tan gular\text{ prism}}=2(21+15+35) \\ \text{Area}_{rec\tan gular\text{ prism}}=2(71) \\ \text{Area}_{rec\tan gular\text{ prism}}=142 \end{gathered}$

Step 3

finally, add the areas to find the total

$\begin{gathered} Area_{total}=Area_1+Area_2 \\ Area_{total}=38In^2+143in^2 \\ Area_{total}=181\text{ square inches} \end{gathered}$

I hope this helps you