What is the standard formula for the surface area of a rectangular prism with length l, width w, and height h?

What is the standard formula for the surface area of a rectangular prism with length l, width w, and height h?

• A. 2(lw + lh + wh)
• B. lw + lh + wh
• C. 2(lw) + 2(h)
• D. l w h

Answer: (A)

Surface area is found by adding the areas of all six faces of a rectangular prism. There are two faces with area lw, two with area lh, and two with area wh. So the total is 2(lw) + 2(lh) + 2(wh), which factors to 2(lw + lh + wh). This is why the standard formula is 2(lw + lh + wh). Expressions like lw + lh + wh miss the factor of 2 because they count only one of each face, 2(lw) + 2(h) leaves out a pair of faces, and l w h is the volume, not the surface area.

Surface area is found by adding the areas of all six faces of a rectangular prism. There are two faces with area lw, two with area lh, and two with area wh. So the total is 2(lw) + 2(lh) + 2(wh), which factors to 2(lw + lh + wh). This is why the standard formula is 2(lw + lh + wh). Expressions like lw + lh + wh miss the factor of 2 because they count only one of each face, 2(lw) + 2(h) leaves out a pair of faces, and l w h is the volume, not the surface area.