Scale Drawings & Similar Figures • Topic 2 of 2

Area Ratio vs Side Length Ratio

When two figures are similar with side length ratio = k, their areas have a squared relationship:

Area Ratio = k^2

Similarly, if you know the area ratio, the side length ratio = square root of the area ratio.

Side Ratio (k)	Area Ratio (k^2)
1:2	1:4
1:3	1:9
2:5	4:25

SCALE FACTOR EFFECT ON AREA:

Square 1 (k=1)    Square 2 (k=2)    Square 3 (k=3)
  1cm x 1cm        2cm x 2cm         3cm x 3cm
  Area = 1cm^2     Area = 4cm^2      Area = 9cm^2

  k=2 -> Area ratio = 4 = 2^2
  k=3 -> Area ratio = 9 = 3^2

Solved Examples

Worked Example

Triangle A has side 4cm, similar triangle B has side 12cm. Area of A = 8cm^2. Find area of B.

Solutionk = 12/4 = 3. Area ratio = 3^2 = 9. Area of B = 8 x 9 = 72cm^2.

Worked Example

Two similar hexagons have areas 25cm^2 and 100cm^2. Find the side length ratio.

SolutionArea ratio = 100/25 = 4. k^2 = 4, so k = 2. Side ratio = 1:2.

Key Points

Side ratio k -> Area ratio k^2
Area ratio -> Side ratio = square root of area ratio
Scale factor applies to all linear measurements (sides, perimeter, height)
Area scales with the square of the scale factor

Quick Check — 4 MCQs

Tap an option to check your answer0 / 4

Q1.If the side ratio of two similar figures is $k$, the area ratio is:

Explanation: Area $\propto k^2$.

Q2.If the side ratio is $2:3$, the area ratio is:

Explanation: $2^2:3^2$.

Q3.Doubling the sides makes the area:

Explanation: $2^2=4$.

Q4.The perimeter ratio of similar figures equals the:

Explanation: Same as side ratio.

Practice more MCQs → 📝 Assignment · 35 marks