How to Calculate Missing Length When You Have Total Surface Area

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The surface area of a solid, or three-dimensional shape, is the sum of the areas of all of the faces of the solid. Surface area problems that involve a missing length usually refer to cuboid shapes. Cuboids are cubes and rectangular versions of cubes. To solve for the missing length, it is important to remember the area formulas for the various faces of the solid. For cuboids, all of the faces are rectangles, so the area of each face is equal to the product of two perpendicular sides of the face.

Calculate the areas of the two faces that do not involve the missing length, "L." The area of each face is equal to the product of the base times the height of that face.

Add the two products calculated in Step 1.

Subtract the sum calculated in Step 2 from the total surface area given in the problem.

Calculate the areas of the four faces that involve the missing length. The area of each face is equal to the product of the base times the height of that face. Leave the areas in terms of "L."

Add the four products calculated in Step 1. Leave the sum in terms of "L."

Divide the difference found in Step 3 by the coefficient of the sum from Step 5. The quotient is equal to the missing length.

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