Answer:
[tex]360\ cm^2[/tex]
Step-by-step explanation:
Step 1: Determine the area of the bottom rectangle
[tex]A = l * w[/tex]
[tex]A = 10\ cm * 12\ cm[/tex]
[tex]A = 120\ cm^2[/tex]
Step 2: Determine the area of the back rectangle
[tex]A = l * w[/tex]
[tex]A = 10\ cm * 5\ cm[/tex]
[tex]A = 50\ cm^2[/tex]
Step 3: Determine the area of the top rectangle
[tex]A = l * w[/tex]
[tex]A = 10\ cm * 13\ cm[/tex]
[tex]A = 130\ cm^2[/tex]
Step 4: Determine the area of the triangle
[tex]A = \frac{h*b}{2}[/tex]
[tex]A = \frac{5\ cm * 12\ cm}{2}[/tex]
[tex]A = \frac{60\ cm^2}{2}[/tex]
[tex]A = 30\ cm^2[/tex]
Step 5: Determine the surface area
[tex]120\ cm^2 + 50\ cm^2 + 130\ cm^2 + 2(30\ cm^2)[/tex]
[tex]360\ cm^2[/tex]
Answer: [tex]360\ cm^2[/tex]
