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:
- Measure or identify the length, width, and height of the prism.
- Calculate the area of each pair of faces:
- lwlwlw
- lhlhlh
- whwhwh
- Add these three areas together.
- Multiply the sum by 2.
- 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
