To find the surface area of a rectangular prism, you add the areas of all six rectangular faces using a simple formula:
Surface area=2(lw+lh+wh)\text{Surface area}=2(lw+lh+wh)Surface area=2(lw+lh+wh)

What a rectangular prism is

A rectangular prism is a 3D box shape with:

  • Length lll
  • Width (or breadth) www
  • Height hhh

Each face is a rectangle, and there are 6 faces total.

The key surface area formula

Every pair of opposite faces is the same size. So we group them in pairs:

  • Front and back: each has area l×hl\times hl×h
  • Left and right: each has area w×hw\times hw×h
  • Top and bottom: each has area l×wl\times wl×w

Add them all:

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

This gives the total surface area in square units.

Step‑by‑step method (recipe style)

  1. Write down the three dimensions
    • Identify which number is length, width, and height. They must all be in the same unit (all cm, all m, etc.).
  1. Multiply the dimensions in pairs
    • Compute lwlwlw
    • Compute lhlhlh
    • Compute whwhwh
  1. Add those three results
    • Find lw+lh+whlw+lh+whlw+lh+wh.
  1. Double the total
    • Multiply by 2 to account for the opposite faces:
      Surface area=2(lw+lh+wh)\text{Surface area}=2(lw+lh+wh)Surface area=2(lw+lh+wh).
  1. Attach proper units
    • If the dimensions are in cm, the surface area is in cm2\text{cm}^2cm2; if in m, then m2\text{m}^2m2.

Example you can copy

Say a rectangular prism has:

  • l=4l=4l=4 cm
  • w=3w=3w=3 cm
  • h=5h=5h=5 cm
  1. Multiply in pairs:
    • lw=4×3=12lw=4\times 3=12lw=4×3=12
    • lh=4×5=20lh=4\times 5=20lh=4×5=20
    • wh=3×5=15wh=3\times 5=15wh=3×5=15
  1. Add them:
    • 12+20+15=4712+20+15=4712+20+15=47
  1. Double the sum:
    • 2×47=942\times 47=942×47=94

So the surface area is 94textcm294\\text{cm}^294textcm2.

Quick mental shortcut

A common “shortcut” teachers share is:

  • Compute lwlwlw, lhlhlh, whwhwh
  • Add them
  • Multiply by 2

It’s exactly the same as the full formula, just remembered as “multiply in pairs, add, then times 2.”

Common mistakes to avoid

  • Mixing units (like cm and m together). Convert everything to one unit first.
  • Forgetting to multiply by 2, which gives only half the surface area.
  • Confusing surface area with volume (volume uses lwhlwhlwh, surface area uses 2(lw+lh+wh)2(lw+lh+wh)2(lw+lh+wh)).

Mini “latest” angle

Rectangular prism problems keep showing up in middle school and early high school math curricula and online homework help discussions, especially as students prep for standardized tests in 2025–2026. The same core formula still rules them all: 2(lw+lh+wh)2(lw+lh+wh)2(lw+lh+wh).

TL;DR:
Multiply the three dimensions in pairs, add them, and double:
Surface area=2(lw+lh+wh)\text{Surface area}=2(lw+lh+wh)Surface area=2(lw+lh+wh).

Information gathered from public forums or data available on the internet and portrayed here.