Scaling in Space Math Example 1

Follow the full solution, then compare it with the other examples linked below.

easy

A square has side length 3 cm. If all lengths are doubled (scale factor

k=2

), what are the new perimeter and area?

1
Step 1: Original side = 3 cm. New side $= 3 \times 2 = 6$ cm.
2
Step 2: Perimeter scales by $k$ : new perimeter $= 4 \times 6 = 24$ cm (original was $12$ cm, doubled).
3
Step 3: Area scales by $k^2$ : original area $= 9$ cm², new area $= 9 \times 4 = 36$ cm².
4
Step 4: Verify: $6^2 = 36$ cm².

Answer

New perimeter = 24 cm; new area = 36 cm².

When a shape is scaled by factor

k

: all lengths multiply by

k

, all areas multiply by

k^2

, and all volumes multiply by

k^3

. This is because area is two-dimensional (two lengths multiplied) and volume is three-dimensional.

About Scaling in Space

How length, area, and volume measurements change when a figure is uniformly enlarged or shrunk by a scale factor.

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