Calculate the lateral surface area of a triangular prism with a base that has sides 6, 5, and 6 units, and a height of 12 units.

The length of the prism is 12 units. This will be one dimension for all rectangular faces.
The other dimension for each rectangular face is the corresponding side of the triangular base.

• Rectangle 1: Corresponds to Side 1 of the triangle.

  • Length = 12
  • Width = Side 1 = 6

• Rectangle 2: Corresponds to Side 2 of the triangle.

  • Length = 12
  • Width = Side 2 = 5

• Rectangle 3: Corresponds to Side 3 of the triangle.

  • Length = 12
  • Width = Side 3 = 6

The area of a rectangle is given by the formula $A = \text{length} \times \text{width}$.

$$A_{\text{Rectangle 1}} = 12 \times 6$$ $$A_{\text{Rectangle 1}} = 72$$

The area of Rectangle 1 is $\boxed{\text{72 square units}}$.

$$A_{\text{Rectangle 2}} = 12 \times 5$$ $$A_{\text{Rectangle 2}} = 60$$

The area of Rectangle 2 is $\boxed{\text{60 square units}}$.

$$A_{\text{Rectangle 3}} = 12 \times 6$$ $$A_{\text{Rectangle 3}} = 72$$

The area of Rectangle 3 is $\boxed{\text{72 square units}}$.