calculate the surface area of the composite figure shown.\nback prism:\n1 base: 8 by 8\n4 lateral faces: 8…

calculate the surface area of the composite figure shown.\nback prism:\n1 base: 8 by 8\n4 lateral faces: 8 by 2\none shared base: 64 - 32 = 32 square units\nfront prism:\n1 base: 8 by 4\n2 lateral faces: 8 by 2\n2 lateral faces: 2 by 4\none shared base: area covered by other prism\ntotal surface area:

calculate the surface area of the composite figure shown.\nback prism:\n1 base: 8 by 8\n4 lateral faces: 8 by 2\none shared base: 64 - 32 = 32 square units\nfront prism:\n1 base: 8 by 4\n2 lateral faces: 8 by 2\n2 lateral faces: 2 by 4\none shared base: area covered by other prism\ntotal surface area:

Answer

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)