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Two similar shapes, one scale factor, three different powers: lengths scale by it, areas by its square, volumes by its cube. Enter the matching pair of lengths and the measurement you want scaled, and the right power is chosen and named, which is the entire trick of these questions.

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    Worked Example

    Two similar shapes have matching sides of 8 cm and 12 cm. The small one has area 10 cm². Find the big area.

    1. Scale factor:12 ÷ 8 = 1.5
    2. Areas scale by SF²:1.5² = 2.25
    3. Multiply:10 × 2.25 = 22.5

    Answer: 22.5 cm²

    Try These Yourself

    Matching sides 5 cm and 15 cm. A small length of 4 cm becomes?Show answerHide answer

    Answer: 12 cm

    SF is 3, and lengths use it plainly.

    SF is 2. The small volume is 30 cm³. Big volume?Show answerHide answer

    Answer: 240 cm³

    Volumes scale by 2³ = 8.

    SF is 3. The big area is 90 cm². Small area?Show answerHide answer

    Answer: 10 cm²

    Going down, divide by 3² = 9.