Question

calculate the surface area of the composite figure shown.
back prism:
1 base: 8 by 8
4 lateral faces: 8 by 2
one shared base: 64 - 32 = 32 square units
front prism:
1 base: 8 by 4
2 lateral faces: 8 by 2
2 lateral faces: 2 by 4
one shared base: area covered by other prism
total surface area:

Explanation:

Step1: Calculate the surface area of the back prism

• Base: \(8\times8 = 64\)
• Lateral faces: \(4\times(8\times2)=4\times16 = 64\)
• Total for back prism: \(64 + 64=128\)

Step2: Calculate the surface area of the front prism

• Base: \(8\times4 = 32\)
• Lateral faces: \(2\times(8\times2)+2\times(2\times4)=32 + 16=48\)
• Shared base (subtract): \(32\)
• Total for front prism: \(32+48 - 32=48\)

Step3: Sum up the surface areas

• Total surface area: \(128+48=176\)

Answer:

\(176\)