For a rectangular solid with length l, width w, and height h, which expression gives its surface area?

For a rectangular solid with length l, width w, and height h, which expression gives its surface area?

• A. SA = 2lw + 2hw + 2hl
• B. SA = lw + hw + hl
• C. SA = 4(lw + hw + hl)
• D. SA = wlh

Answer: (A)

Surface area is found by adding the areas of all six faces of a rectangular solid. There are two faces with area lw, two with area wh, and two with area lh. Summing these gives 2lw + 2wh + 2lh, which can be written as 2(lw + wh + lh). This is the correct expression because it accounts for every face twice (each pair of opposite faces has the same area). The other forms miss those doubles, overcount by too much, or give the volume (lwh) instead of surface area.

Surface area is found by adding the areas of all six faces of a rectangular solid. There are two faces with area lw, two with area wh, and two with area lh. Summing these gives 2lw + 2wh + 2lh, which can be written as 2(lw + wh + lh). This is the correct expression because it accounts for every face twice (each pair of opposite faces has the same area). The other forms miss those doubles, overcount by too much, or give the volume (lwh) instead of surface area.