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

Definition of Surface Area

Surface Area: Total area of the outside part or layer of a 3D figure.
For rectangular prisms, which have six faces, calculate the area of each face and sum them to find the total surface area.

Surface Area Formula:
- ( \text{Surface Area} = 2 \times \text{front/back} + 2 \times \text{right/left} + 2 \times \text{top/bottom} )
Each face pair is multiplied by 2 because opposite faces have the same area.

Front/Back Faces:
- Example: For the front face, use a 6 by 2 rectangle.
- Formula: ( \text{Area} = \text{length} \times \text{width} )
- Calculate: ( 6 \times 2 = 12 ) square inches.
- Total for front and back: ( 2 \times 12 = 24 ) square inches.
Right/Left Faces:
- Example: For the right face, use a 3 by 2 rectangle.
- Calculate: ( 3 \times 2 = 6 ) square inches.
- Total for right and left: ( 2 \times 6 = 12 ) square inches.
Top/Bottom Faces:
- Example: For the top face, use a 6 by 3 rectangle.
- Calculate: ( 6 \times 3 = 18 ) square inches.
- Total for top and bottom: ( 2 \times 18 = 36 ) square inches.

Sum of all face areas:
- Front/Back: 24 square inches
- Right/Left: 12 square inches
- Top/Bottom: 36 square inches
Total Surface Area:
- ( 24 + 12 + 36 = 72 ) square inches.

To find the surface area of a rectangular prism, calculate the area of each face and sum them.
Visual aids like a net can help in understanding the layout and calculations.

Thanks for watching and learning about how to calculate the surface area of a rectangular prism. Until next time!