Math with Mr. J: Finding the Surface Area of a Rectangular Prism

Introduction

• Surface Area: Total area of the outside part or layer of a 3D figure.
• Rectangular Prisms: Have six faces; find the area of each face and sum them up to get the surface area.

Surface Area Formula for Rectangular Prism

• Formula: Surface area = 2 × (front or back) + 2 × (right or left) + 2 × (top or bottom)
  • Multiply by 2 because opposite faces are identical (e.g., front and back).

Finding Surface Area: Step-by-Step

1. Front or Back

   • Example: Front face is 6 x 2 (length x width).
   • Area = 6 x 2 = 12 square inches.
   • Since back is identical, we multiply by 2: 2 x 12 = 24 square inches.

2. Right or Left

   • Example: Right face is 3 x 2.
   • Area = 3 x 2 = 6 square inches.
   • Multiply by 2 for left side: 2 x 6 = 12 square inches.

3. Top or Bottom

   • Example: Top face is 6 x 3.
   • Area = 6 x 3 = 18 square inches.
   • Multiply by 2 for bottom: 2 x 18 = 36 square inches.

Calculating Total Surface Area

• Sum all combined areas:
  • Front and Back: 24 square inches.
  • Right and Left: 12 square inches.
  • Top and Bottom: 36 square inches.
• Total Surface Area = 24 + 12 + 36 = 72 square inches.

Summary

• To find the surface area of a rectangular prism, calculate the area of each face and sum them.
• Key point: Opposite faces are identical, which is why we multiply by 2 in the formula.

Conclusion

• The surface area of the rectangular prism in the example is 72 square inches.
• Remember, understanding the layout (using a net) helps visualize and solve surface area problems effectively.

Note: The explanation included a net of the prism to visualize all faces laid out in 2D.