The formula for the surface area of a right rectangular prism is A  2lw  2hw  2lh, where l, w, and h represent the length, width, and height, respectively. Which term of this formula is not dependent on the height?

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Mathematics

5 December, 06:35

The formula for the surface area of a right rectangular prism is A  2lw  2hw  2lh, where l, w, and h represent the length, width, and height, respectively. Which term of this formula is not dependent on the height?

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Krystal Mitchell · Answer 1

The term 2lw is independent of the height

Step-by-step explanation:

This formula is usually obtained reasoning like this: the rectangular prism has 6 faces, thus the surface area is the sum of the areas of these faces.

2 faces are l*w rectangles, so their area is lw+lw=2lw. Note that we are not using the height to compute the area, then this is the independent term.

The 4 remaining rectangles involve the height as one of their dimensions, so their areas (2hw+2lh) depend on the height.