"Surface area of a cube or a rectangular prism"

Surface Area of a Rectangular Prism

  • Definition: The surface area of a rectangular prism is the total area of all six faces of the prism.

  • Components of a Rectangular Prism: A rectangular prism has three pairs of opposite faces:

    • Front and Back faces
    • Top and Bottom faces
    • Left and Right faces

Finding the Surface Area

  1. Calculate Area of Each Face:

    • Front Face:

      • Dimensions: 5 cm×6 cm5 \text{ cm} \times 6 \text{ cm}
      • Area: 5×6=30 cm25 \times 6 = 30 \text{ cm}^2

    • Back Face: Same as Front Face

      • Area: 30 cm230 \text{ cm}^2

    • Top Face:

      • Dimensions: 5 cm×4 cm5 \text{ cm} \times 4 \text{ cm}
      • Area: 5×4=20 cm25 \times 4 = 20 \text{ cm}^2

    • Bottom Face: Same as Top Face

      • Area: 20 cm220 \text{ cm}^2

    • Right Face:

      • Dimensions: 4 cm×6 cm4 \text{ cm} \times 6 \text{ cm}
      • Area: 4×6=24 cm24 \times 6 = 24 \text{ cm}^2

    • Left Face: Same as Right Face

      • Area: 24 cm224 \text{ cm}^2

  2. Total Surface Area Calculation:

    • Surface Area Formula:
      Surface Area=2×(Area of Front+Area of Top+Area of Right)\text{Surface Area} = 2 \times (\text{Area of Front} + \text{Area of Top} + \text{Area of Right})
    • Substitute the calculated areas:
    • Surface Area=2×(30+20+24)\text{Surface Area} = 2 \times (30 + 20 + 24)
    • Surface Area=2×74=148 cm2\text{Surface Area} = 2 \times 74 = 148 \text{ cm}^2
Answer:
  • The surface area of the rectangular prism is 148 cm2148 \text{ cm}^2.