Answer:
[tex]S=1964 in^{2}[/tex]
Step-by-step explanation:
The surface of a rectangular prims is defined as
[tex]S=2lw+2wh+2lh[/tex]
Where [tex]l[/tex] is length, [tex]w[/tex] is width and [tex]h[/tex] is height.
In this case, we have a figure formed by two rectangular prism. We are gonna call Surface 1 to the bottoming prism.
Its diemensions are:
[tex]l=24in\\w=10in\\h=8in[/tex]
So, the Surface 1 is
[tex]S_{1}=2(24)(10)+2(10)(8)+2(24)(8)= 480+160+384=1024in^{2}[/tex]
Now, the dimensions of Surface 2 are
[tex]l=9in\\w=10in\\h=20in[/tex]
Replacing all values, its surface is
[tex]S_{2}= 2(9)(10)+2(10)(20)+2(9)(20)=180+400+360=940in^{2}[/tex]
Therefore, the total surface of the whole figure is
[tex]S=1024+940=1964 in^{2}[/tex]
