50 Finding Scale Factor Worksheet - Free Printable

Let’s solve each problem step by step.

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Problem 1: Two Right Triangles

Left triangle:
- Base = 16 m
- Height = 12 m

Area of a triangle = (base × height) ÷ 2
→ Area = (16 × 12) ÷ 2 = 192 ÷ 2 = 96 m²

Right triangle:
- Height = 24 m
- We need to find the base. Since it’s scaled from the left triangle, we can use scale factor first.

Scale Factor: Compare corresponding sides.
Height went from 12 m → 24 m → that’s ×2
So scale factor = 2

Then base must also be scaled by 2: 16 m × 2 = 32 m

Now area of right triangle = (32 × 24) ÷ 2 = 768 ÷ 2 = 384 m²

Check: When you scale a shape by factor k, area scales by k².
Here k=2, so area should be 96 × 4 = 384 → matches! ✔

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Problem 2: Two Rectangles

Left rectangle:
- Length = 12 mm
- Width = 9 mm

Area = length × width = 12 × 9 = 108 mm²

Right rectangle:
- One side is given as 4 mm. Which side? Looking at the drawing, it’s the shorter side — so likely the width.
Original width was 9 mm → now 4 mm? That doesn’t match scaling evenly.

Wait — let’s check both dimensions.

If the right rectangle has width = 4 mm, and original width = 9 mm, then scale factor would be 4/9 — but then length should be 12 × (4/9) = 5.333... which isn’t shown.

But in the image, the right rectangle looks like it’s scaled down proportionally. Let’s assume the 4 mm is the *length* (since it’s labeled under the long side).

Original length = 12 mm → new length = 4 mm → scale factor = 4/12 = 1/3

Then width should be 9 mm × (1/3) = 3 mm

Area of right rectangle = 4 × 3 = 12 mm²

Check with area scaling: original area 108, scale factor 1/3 → area scales by (1/3)² = 1/9 → 108 ÷ 9 = 12 → matches! ✔

So scale factor = 1/3

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Problem 3: Two Circles

Left circle: radius r = 4 in
Use π = 3.14

Area = πr² = 3.14 × 4² = 3.14 × 16 = 50.24 in²

Right circle: radius r = 12 in

Scale factor: 12 ÷ 4 = 3

Area = 3.14 × 12² = 3.14 × 144 = let’s calculate:

3.14 × 100 = 314
3.14 × 40 = 125.6
3.14 × 4 = 12.56
Total = 314 + 125.6 = 439.6 + 12.56 = 452.16 in²

Check with scaling: area scales by 3² = 9 → 50.24 × 9 = ?

50 × 9 = 450
0.24 × 9 = 2.16
Total = 452.16 → matches! ✔

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Final Answer:

1. Left Area: 96 m², Scale Factor: 2, Right Area: 384 m²
2. Left Area: 108 mm², Scale Factor: 1/3, Right Area: 12 mm²
3. Left Area: 50.24 in², Scale Factor: 3, Right Area: 452.16 in²