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 calculates the sum of the areas of all six faces of the prism. Each pair of opposite faces has the same area: two faces are l×wl\times wl×w, two are l×hl\times hl×h, and two are w×hw\times hw×h. Multiplying each area by 2 and then adding them gives the total surface area
Steps to calculate surface area:
- Measure or identify the length, width, and height of the prism.
- Calculate the area of each pair of faces:
- Top and bottom: l×wl\times wl×w
- Front and back: l×hl\times hl×h
- Left and right: w×hw\times hw×h
- Add these areas and multiply by 2:
2(lw+lh+wh)2(lw+lh+wh)2(lw+lh+wh)
- The result is the total surface area, expressed in square units (e.g., square centimeters, square inches)
Example:
If a rectangular prism has length = 8 inches, width = 5 inches, and height = 3 inches, then:
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 means the total surface area is 158 square inches
. You can also visualize the prism as a net (flattened out shape) and calculate the area of each rectangle face, then sum them up
. In summary, the key is to find the areas of the three distinct rectangular faces and double their sum to get the total surface area of the rectangular prism.
