Rectangular Prism Surface Area

Rectangular Prism

Definition

• A rectangular prism is a three-dimensional figure that has three pairs of rectangular faces, where each pair of opposite faces has the same dimensions for length and width.

Properties

• It has three sets or pairs of sides:

  • Length (l)

  • Width (w)

  • Height (h)

Surface Area Formula

• The formula for calculating the surface area (SA) of a rectangular prism is given by:

  • $SA = 2lw + 2wh + 2hl$
    or equivalently:

  • $SA = 2(lw + wh + hl)$

Components of the Formula

1. First term: $2lw$

   • Represents the area of the two faces with dimensions length and width.

2. Second term: $2wh$

   • Represents the area of the two faces with dimensions width and height.

3. Third term: $2hl$

   • Represents the area of the two faces with dimensions height and length.

Example Calculation

• Given:

  • Length (l) = 10 cm

  • Width (w) = 3 cm

  • Height (h) = 2 cm

• Substitute values into the surface area formula:

  • $SA = 2 imes 10 imes 3 + 2 imes 3 imes 2 + 2 imes 2 imes 10$

• Break down the calculations:

  • First part: $2 imes 10 imes 3 = 60$

  • Second part: $2 imes 3 imes 2 = 12$

  • Third part: $2 imes 2 imes 10 = 40$

• Combine these results:

  • $SA = 60 + 12 + 40$

  • $SA = 112 ext{ square centimeters}$

Conclusion

• The surface area of the given rectangular prism is 112 square centimeters.