Geometry and TrigonometryMediumSurface area of a rectangular box
Geometry and Trigonometry practice question
A closed rectangular box has dimensions 4 by 5 by 6. What is its total surface area?
- A. 148Correct
- B. 120
- C. 74
- D. 296
Answer: A. 148
A box has three pairs of identical faces: 4 × 5, 4 × 6 and 5 × 6. Surface area is 2(20 + 24 + 30) = 2(74) = 148.
Why the other answers are wrong
- B. 120
- 120 is the VOLUME, 4 × 5 × 6. Surface area adds the areas of the faces.
- C. 74
- 74 is the area of one face of each pair. The box has two of each, so double it.
- D. 296
- 296 doubles the total twice. Each of the three face areas is counted exactly twice: 2 × 74.
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