how do you find the surface area of a rectangular prism

how do you find the surface area of a rectangular prism

1 month ago 7
Nature

To find the surface area of a rectangular prism, you use the formula:

SA=2lw+2lh+2whSA=2lw+2lh+2whSA=2lw+2lh+2wh

where:

  • lll = length,
  • www = width,
  • hhh = height.

This formula calculates the area of all six rectangular faces of the prism by adding the areas of the three pairs of identical faces (length × width, length × height, and width × height) and doubling each because each pair has two faces

. Steps to calculate surface area:

  1. Measure or identify the length, width, and height of the rectangular prism.
  2. Calculate the area of each pair of faces:
    • lwlwlw for the top and bottom,
    • lhlhlh for the front and back,
    • whwhwh for the two sides.
  3. Multiply each area by 2 (since there are two of each face).
  4. Add all these values together to get the total surface area.

Example: If a rectangular prism has length 5 cm5,cm5cm, width 3 cm3,cm3cm, and height 4 cm4,cm4cm, then:

SA=2(5×3)+2(5×4)+2(3×4)=2(15)+2(20)+2(12)=30+40+24=94 cm2SA=2(5\times 3)+2(5\times 4)+2(3\times 4)=2(15)+2(20)+2(12)=30+40+24=94,cm^2SA=2(5×3)+2(5×4)+2(3×4)=2(15)+2(20)+2(12)=30+40+24=94cm2

So, the surface area is 94 square centimeters

. This method ensures you account for all six faces of the prism to find the total surface area accurately

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