A rectangular prism has dimensions 4 cm, 6 cm, and 9 cm. If the dimensions are scaled up by a factor of 2, what is the new surface area?

Sat, 18 Apr 2026 08:39:37 +0000

**Why Scaling Rectangular Prisms Matters in Real-Life Applications**
Curious about how dimensions affect space, cost, and functionality? The simple rectangular prism—measuring 4 cm, 6 cm, and 9 cm—serves as a foundational model across construction, packaging, and design. When scaled up by a factor of 2, understanding its new surface area unlocks insights vital for decision-making. This rise in geometric awareness reflects broader trends in precise measurements used in manufacturing, logistics, and even interior planning—making it a topic gaining quiet traction among users exploring practical design and resource efficiency. **Is Scaling Up a Rectangular Prism by 2x Just Double Each Side?**
When any linear dimension of a rectangular prism is scaled by a factor of 2, every edge—length, width, and height—increases proportionally. The original dimensions—4 cm, 6 cm, and 9 cm—expand to 8 cm, 12 cm, and 18 cm respectively. This scaling directly impacts surface area, which quadruples not just linearly, but through a more complex formula. Scaling affects such spatial properties because surface area depends quadratically on length and width, amplifying the effect of growth across all three dimensions. **How to Calculate the New Surface Area**
The surface area of a rectangular prism is calculated with the formula:
Surface Area = 2(lw + lh + wh)
Using the original dimensions:
Original Surface Area = 2(4×6 + 4×9 + 6×9) = 2(24 + 36 + 54) = 2(114) = 228 cm² After scaling:
New Surface Area = 2(8×12 + 8×18 + 12×18) = 2(96 + 144 + 216) = 2(456) = 912 cm²
From the original 228 cm² to 912 cm², the surface area increases by a factor of 4—confirming the quadratic relationship inherent in scaling.