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# How much exposed surface area needs to be rust-proofed?

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Amy needs to rust-proof a wrought-iron fence made of a rail that is a 1 cm thick by 4 cm wide by 102 cm long rectangular prism supported by posts that are 2 cm by 2 cm by 1 m high rectangular prisms. The posts are spaced 8 cm apart, attach to the bottom of the rail, and are embedded in cement. How much exposed surface area needs to be rust-proofed? May 1, 2020

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If I didn't make an error...

Lateral surface area to be covered of  upright 11  posts =

Note that 1 m  = 100 cm

11  * [ 4* 100 cm * 2 cm]   =

11 [800 cm^2 ] =  =

8800 cm^2

Suface area of top rail to be coated  =

( Lateral surface area of rail ) -   area where the upright post meets the top rail

(Area at two ends of the top rail  + lateral surface area of rail )  -  11 (2cm *2cm)  =

2 ( 1cm* 4cm)  + 2*102 cm  ( 1cm +  4 cm  ) - 11 ( 4 cm^2)  =

2 (4cm^2) + 204cm (5cm)  - 44 cm^2  =

8cm^2  + 1020cm^2 - 44cm^2  = 984 cm^2

Total suface area to be covered  =   [ 8800+ 984] cm^2  = 9784 cm^2   May 1, 2020