Answer:
[tex]A_{total} = 144\ cm^2[/tex]
Step-by-step explanation:
Step 1: Determine the area of the bottom square
[tex]A = l * w[/tex]
[tex]A = 6\ cm * 6\ cm[/tex]
[tex]A = 36\ cm^2[/tex]
Step 2: Determine the area of the triangle
[tex]A= \frac{h *b}{2}[/tex]
[tex]A=\frac{9\ cm * (6\ cm/2)}{2}[/tex]
[tex]A=\frac{9\ cm * 3\ cm}{2}[/tex]
[tex]A=13.5\ cm^2[/tex]
Since we have two of these right triangles on each side we come out to having 8 of these triangles total since we have 4 sides. We multiply 8 by our area from one triangle.
[tex]A=13.5\ cm^2*8[/tex]
[tex]A = 108\ cm^2[/tex]
Step 3: Determine the surface area
[tex]A_{total} = 36\ cm^2 + 108\ cm^2[/tex]
[tex]A_{total} = 144\ cm^2[/tex]
Answer: [tex]A_{total} = 144\ cm^2[/tex]
