Question

question 10 of 10
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. true
b. false

Explanation:

Step1: Recall surface area formula

For a three - dimensional figure (e.g., a prism), the lateral surface area \(LSA\) is given by \(LSA = \text{Perimeter of the base}(P)\times\text{height}(h)\). But the total surface area \(TSA\) is \(TSA= LSA + 2\times\text{Area of the base}(B)\), i.e., \(TSA=Ph + 2B\).

Step2: Analyze the statement

The given statement says “to find the surface area... multiply perimeter of a face by the height”. It ignores the area of the two bases (in case of prisms) or other components (for other 3D figures like cylinders, where lateral surface area is \(2\pi rh\) and total surface area is \(2\pi rh+2\pi r^{2}\)). So the statement is too simplistic and incorrect for calculating the total surface area of a three - dimensional figure.

Answer:

B. False