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

Surface Area=2(lw+lh+wh)\text{Surface Area}=2(lw+lh+wh)Surface Area=2(lw+lh+wh)

where:

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

This formula works because a rectangular prism has six faces: three pairs of identical rectangles. The areas of these pairs are:

• length × width (top and bottom),
• length × height (front and back),
• width × height (left and right).

You calculate the area of each pair, sum them, and multiply by 2 to account for both faces in each pair

. Step-by-step:

1. Measure or identify the length, width, and height of the prism.
2. Calculate the area of each pair of faces:
   • lwlwlw
   • lhlhlh
   • whwhwh
3. Add these three areas together.
4. Multiply the sum by 2.
5. The result is the total surface area.

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

. Alternatively, you can find the surface area by drawing a net of the prism, calculating the area of each rectangle, and adding them up, but using the formula is faster and more straightforward