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

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

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Answer 1 · 2016-01-09T14:56:43

$SA = 2 (w l + l h + h w)$ $"SA"=2(wl+lh+hw)$

Explanation:

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

$SA = 2 (w l + l h + h w)$ $"SA"=2(wl+lh+hw)$

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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 $w l$ $wl$ , another is just $l h$ $lh$ , and the other $h w$ $hw$ . Since there are two of each, that is reflected in the formula by the multiplication by $2$ $2$ .

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

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The blue rectangles are $2 \cdot w l$ $2*wl$ .

The yellow rectangles are $2 \cdot l h$ $2*lh$ .

The red rectangles are $2 \cdot h w$ $2*hw$ .

Again, the surface area would be

$SA = 2 w l + 2 l h + 2 h w$ $"SA"=2wl+2lh+2hw$

$= 2 (w l + l h + h w)$ $=2(wl+lh+hw)$

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

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