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 areas of different parts

• Back Prism:
• Base: \(8\times8 = 64\)
• Lateral faces: \(4\times(8\times2)=4\times16 = 64\)
• Front Prism:
• Base: \(8\times4=32\)
• Lateral faces: \(2\times(8\times2)+2\times(2\times4)=32 + 16=48\)
• Shared base (not included in total): \(64 - 32=32\) (already accounted for in back prism base)

Step2: Sum up the areas

$$64+64 + 32+48=208$$

Answer:

\(208\)