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 adds the areas of all six faces of the prism: two each of length × width, length × height, and width × height
Step-by-step method:
- Measure or identify the length, width, and height of the rectangular prism.
- 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
- Multiply each area by 2 (since each pair has two faces).
- Add all these values together to get the total surface area:
2(lw)+2(lh)+2(wh)2(lw)+2(lh)+2(wh)2(lw)+2(lh)+2(wh)
Example:
If a rectangular prism has length = 8 inches, width = 5 inches, and height = 3 inches:
SA=2(8×5)+2(8×3)+2(5×3)=2(40)+2(24)+2(15)=80+48+30=158 square inchesSA=2(8\times 5)+2(8\times 3)+2(5\times 3)=2(40)+2(24)+2(15)=80+48+30=158\text{ square inches}SA=2(8×5)+2(8×3)+2(5×3)=2(40)+2(24)+2(15)=80+48+30=158 square inches
This is the total surface area of the prism
. In summary, to find the surface area of a rectangular prism, calculate the area of each face, double it for the opposite face, and sum all these areas using the formula 2(lw+lh+wh)2(lw+lh+wh)2(lw+lh+wh)
