FTCE Professional Education Practice Exam

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Which formula correctly represents the total surface area of a rectangular solid?

2L + 2W + 2H
2LW + 2WH + 2LH
LWH
LW + LH + WH

The correct answer is: 2LW + 2WH + 2LH

The total surface area of a rectangular solid, also known as a rectangular prism, is determined by calculating the area of each of its six rectangular faces. A rectangular solid has three pairs of opposite faces: the length (L), width (W), and height (H). Each pair contributes to the total surface area. To derive the correct formula, consider the following: 1. There are two faces with dimensions L and W, and the area of these faces combined is 2LW. 2. There are two faces with dimensions W and H, contributing an area of 2WH. 3. Finally, there are two faces with dimensions L and H, which contribute an area of 2LH. When you sum these areas together, you arrive at the formula for the total surface area: 2LW + 2WH + 2LH. This formula effectively accounts for the entirety of the surface area of the rectangular solid by including all the necessary dimensions and their respective contributions, hence making it the correct representation. The other options do not represent the total surface area appropriately. For instance, while LWH represents the volume of the solid, it does not include any surface area calculations.