Answer:
Option B, [tex]396\ units^2[/tex]
Step-by-step explanation:
Step 1: Determine the area of the bottom
[tex]A = l * w[/tex]
[tex]A = 12\ units * 8\ units[/tex]
[tex]A = 96\ units^2[/tex]
Step 2: Determine the area of the back
[tex]A = l * w[/tex]
[tex]A = 9\ units * 8\ units[/tex]
[tex]A = 72\ units^2[/tex]
Step 3: Determine the hypotenuse
Pythagorean theorem → [tex]a^2 + b^2 = c^2[/tex]
[tex]12^2 + 9^2 = c^2\\[/tex]
[tex]144 + 81 = c^2[/tex]
[tex]225 = c^2[/tex]
[tex]\sqrt{225} = \sqrt{c^2}[/tex]
[tex]15 = c[/tex]
Step 4: Determine the area of the top
[tex]A = l * w[/tex]
[tex]A = 15\ units * 8\ units[/tex]
[tex]A = 120\ units^2[/tex]
Step 5: Determine the area of the triangles
[tex]A = \frac{h\ *\ b}{2}[/tex]
[tex]A = \frac{9\ units\ *\ 12\ units}{2}[/tex]
[tex]A = \frac{108\ units^2}{2}[/tex]
[tex]A = 54\ units^2[/tex]
Step 6: Determine the surface area
[tex]96\ units^2 + 72\ units^2 + 120\ units^2 + 2(54\ units^2)[/tex]
[tex]396\ units^2[/tex]
Answer: Option B, [tex]396\ units^2[/tex]
