To find the surface area of a three-dimensional figure, you must find the perimeter of a face and then multiply it by the height.A.TrueB.False

Break Down the Problem

1. Understand the Question: We need to assess whether the statement about finding the surface area of a three-dimensional figure is true or false.
2. Identify Key Terms: Surface area, perimeter of a face, height.

Relevant Concepts

1. Surface Area: The total area of the external surface of a three-dimensional object.
2. Perimeter and Height: The formula for the surface area can vary depending on the shape (e.g., cube, cylinder, etc.). However, generally, the surface area is not solely calculated as the perimeter of one face multiplied by height.

Analysis and Detail

1. Application of Surface Area Formulas:
   • For a rectangular prism, the surface area $SA$ is calculated as: $SA = 2(lw + lh + wh)$
   • For a cylinder, the surface area is given by: $SA = 2\pi r(h + r)$
   • The provided statement oversimplifies the procedure by suggesting that surface area can be computed using just the perimeter of one face and multiplying it by height.

Verify and Summarize

1. Verification of Statement: The statement is inaccurate because the surface area of a three-dimensional figure cannot be generally calculated by just the perimeter of one face and height without considering the other faces or dimensions.

Final Answer

The statement is B. False. The surface area cannot be accurately determined only by finding the perimeter of one face multiplied by the height; the complete dimensions of the figure need to be taken into account.