To find the surface area of a rectangular prism, you use the formula:

SA=2(lw+lh+wh)SA=2(lw+lh+wh)SA=2(lw+lh+wh)

where:

• lll = length,
• www = width,
• hhh = height.

This formula accounts for the areas of all six rectangular faces of the prism: two each of length × width, length × height, and width × height

Step-by-step method:

1. Calculate the area of each pair of opposite faces:
   • Top and bottom: l×wl\times wl×w
   • Front and back: l×hl\times hl×h
   • Left and right sides: w×hw\times hw×h
2. Add these areas together: lw+lh+whlw+lh+whlw+lh+wh.
3. Multiply the sum by 2, since each pair has two faces.

Example:

If a rectangular prism has length 8 inches, width 5 inches, and height 3 inches:

SA=2(8×5+8×3+5×3)=2(40+24+15)=2(79)=158 square inchesSA=2(8\times 5+8\times 3+5\times 3)=2(40+24+15)=2(79)=158\text{ square inches}SA=2(8×5+8×3+5×3)=2(40+24+15)=2(79)=158 square inches

This gives the total surface area of the prism

. In summary, the surface area is found by summing the areas of all the faces, which are rectangles, and then doubling that sum because each face has a matching opposite face.