What is the surface area formula of a 3-dimensional rectangle?

1 Answer
mason m
Jan 9, 2016

#"SA"=2(wl+lh+hw)#

Explanation:

For a rectangular prism with sides #w,l,h#, the surface area is

#"SA"=2(wl+lh+hw)#

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This occurs since there are two pairs of three different faces on every rectangular prism.

Each pair of faces is a different rectangle using two of the the three dimensions of the prism as its own side.

One side is just #wl#, another is just #lh#, and the other #hw#. Since there are two of each, that is reflected in the formula by the multiplication by #2#.

This could also be imagined as a series of flattened-out rectangles:

passyworldofmathematics.com

The blue rectangles are #2*wl#.

The yellow rectangles are #2*lh#.

The red rectangles are #2*hw#.

Again, the surface area would be

#"SA"=2wl+2lh+2hw#

#=2(wl+lh+hw)#

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