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

• The back prism has one base ($8\times8$), four lateral faces ($8\times2$), and one shared base (area covered by other prism).
• Area of the base: $8\times8 = 64$
• Area of the four 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

• The front prism has one base ($8\times4$), two lateral faces ($8\times2$), two lateral faces ($2\times4$), and one shared base (area covered by other prism).
• Area of the base: $8\times4=32$
• Area of the two lateral faces ($8\times2$): $2\times(8\times2)=2\times16 = 32$
• Area of the two lateral faces ($2\times4$): $2\times(2\times4)=2\times8 = 16$
• Total for front prism: $32+32 + 16=80$

Step3: Calculate the total surface area

• Add the surface areas of the back and front prisms: $128+80 = 208$

Answer:

$208$