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. SA = 2(LW + LH + WH)
• B. SA = 2LW + 2LH + 2WH
• C. SA = LW + LH + WH
• D. SA = 4(LW + LH + WH)

Answer: (A)

Surface area is found by adding the areas of all six outside faces. A rectangular prism has two faces for each dimension pair: length by width, length by height, and width by height. So you sum 2 times LW, 2 times LH, and 2 times WH, giving 2LW + 2LH + 2WH, which can be factored as 2(LW + LH + WH). This matches the standard formula. The single terms LW, LH, and WH would miss the opposite faces, and 4(LW + LH + WH) would double-count too much, while 2LW + 2LH + 2WH is just another way of writing the same correct expression.

Surface area is found by adding the areas of all six outside faces. A rectangular prism has two faces for each dimension pair: length by width, length by height, and width by height. So you sum 2 times LW, 2 times LH, and 2 times WH, giving 2LW + 2LH + 2WH, which can be factored as 2(LW + LH + WH). This matches the standard formula. The single terms LW, LH, and WH would miss the opposite faces, and 4(LW + LH + WH) would double-count too much, while 2LW + 2LH + 2WH is just another way of writing the same correct expression.