Answer:
(D) 440 in²
Step-by-step explanation:
We can find the surface area of this complex shape by breaking it down into two smaller shapes:
The base (with side lengths of 10, 10 and 2) and the top (with side lengths of 5, 5, and 8.)
Let's first find the surface area of the base.
The sides of the bass are [tex]10\cdot2 = 20[/tex] in², since there are 4 of these sides, the total side area here is [tex]20\cdot4 = 80[/tex] in².
The bottom of this prism has side lengths of 10 and 10, so [tex]10\cdot10=100[/tex].
There are two of these sides.
[tex]100\cdot2=200[/tex].
Let's add up the side lengths and the base lengths.
[tex]200+80=280[/tex]
We aren't done yet - if we see, the top part is taking away some of that surface area. To find how much it is taking away, we need to find the area of that side.
Note that the side on the base is the exact same as the top, who's side lengths are 5 and 5. So [tex]5\cdot5=25[/tex] in² are being taken away from the base, making it [tex]280-25 = 255[/tex]
Now let's find the surface area of the top.
The side, with lengths of 5 and 8, have a surface area of [tex]5\cdot8=40[/tex] in². Since there are 4 of these sides:
[tex]40\cdot4=160[/tex] in².
Now, the top of the box has side lengths of 5 and 5, so the surface area of that is [tex]5\cdot5 =25[/tex] in².
We don't want to find the area of the bottom of the top prism because that cuts into the base and technically is empty space = no surface area.
Let's add the top and the sides of the top box: [tex]160+25=185[/tex] in².
Finally, let's add the base and the top box surface areas together:
[tex]185 + 255 = 440[/tex]
So the total surface area of this design is 440 in².
Hope this helped (oh my god this took so long to write)
