Answer:
Option B, ![516.3\ units](https://tex.z-dn.net/?f=516.3%5C%20units)
Step-by-step explanation:
<u>Step 1: Determine the area of the back</u>
![A = l * w](https://tex.z-dn.net/?f=A%20%3D%20l%20%2A%20w)
![A = 10\ units * 13\ units](https://tex.z-dn.net/?f=A%20%3D%2010%5C%20units%20%2A%2013%5C%20units)
![A = 130\ units^2](https://tex.z-dn.net/?f=A%20%3D%20130%5C%20units%5E2)
<u>Step 2: Determine the hypotenuse</u>
Pythagorean theorem → ![a^2 + b^2 = c^2](https://tex.z-dn.net/?f=a%5E2%20%2B%20b%5E2%20%3D%20c%5E2)
![(10-6)^2\ units + 7^2\ units = c^2](https://tex.z-dn.net/?f=%2810-6%29%5E2%5C%20units%20%2B%207%5E2%5C%20units%20%3D%20c%5E2)
![4^2\ units + 7^2\ units=c^2](https://tex.z-dn.net/?f=4%5E2%5C%20units%20%2B%207%5E2%5C%20units%3Dc%5E2)
![16\ units+49\ units=c^2](https://tex.z-dn.net/?f=16%5C%20units%2B49%5C%20units%3Dc%5E2)
![\sqrt{65}=\sqrt{c^2}](https://tex.z-dn.net/?f=%5Csqrt%7B65%7D%3D%5Csqrt%7Bc%5E2%7D)
![8.06 = c](https://tex.z-dn.net/?f=8.06%20%3D%20c)
<u>Step 3: Determine the area of the top</u>
![A = l * w](https://tex.z-dn.net/?f=A%20%3D%20l%20%2A%20w)
![A = 13\ units * 8.06\ units](https://tex.z-dn.net/?f=A%20%3D%2013%5C%20units%20%2A%208.06%5C%20units)
![A = 104.81\ units^2](https://tex.z-dn.net/?f=A%20%3D%20104.81%5C%20units%5E2)
<u>Step 4: Determine the area of the front</u>
![A = l * w](https://tex.z-dn.net/?f=A%20%3D%20l%20%2A%20w)
![A = 13\ units * 6\ units](https://tex.z-dn.net/?f=A%20%3D%2013%5C%20units%20%2A%206%5C%20units)
![A = 78\ units^2](https://tex.z-dn.net/?f=A%20%3D%2078%5C%20units%5E2)
<u>Step 5: Determine the area of the bottom</u>
![A = l * w](https://tex.z-dn.net/?f=A%20%3D%20l%20%2A%20w)
![A = 13\ units * 7\ units](https://tex.z-dn.net/?f=A%20%3D%2013%5C%20units%20%2A%207%5C%20units)
![A = 91\ units^2](https://tex.z-dn.net/?f=A%20%3D%2091%5C%20units%5E2)
<u>Step 6: Determine the area of the trapezoid</u>
![A = \frac{a + b}{2} * h](https://tex.z-dn.net/?f=A%20%3D%20%5Cfrac%7Ba%20%2B%20b%7D%7B2%7D%20%2A%20h)
![A = \frac{10\ units\ +\ 6\ units}{2}*7\ units](https://tex.z-dn.net/?f=A%20%3D%20%5Cfrac%7B10%5C%20units%5C%20%2B%5C%206%5C%20units%7D%7B2%7D%2A7%5C%20units)
![A = 8\ units*7\ units](https://tex.z-dn.net/?f=A%20%3D%208%5C%20units%2A7%5C%20units)
![A = 56\ units^2](https://tex.z-dn.net/?f=A%20%3D%2056%5C%20units%5E2)
<u>Step 7: Determine the total surface area</u>
![130\ units^2 + 104.81\ units^2 + 78\ units^2 + 91\ units^2 + 2(56\ units^2)](https://tex.z-dn.net/?f=130%5C%20units%5E2%20%2B%20104.81%5C%20units%5E2%20%2B%2078%5C%20units%5E2%20%2B%2091%5C%20units%5E2%20%2B%202%2856%5C%20units%5E2%29)
![515.81\ units^2](https://tex.z-dn.net/?f=515.81%5C%20units%5E2)
Answer: Option B, ![516.3\ units](https://tex.z-dn.net/?f=516.3%5C%20units)