Maths · Rung 28 of 30

Similarity

Two shapes are similar when they have the same shape and a different size: every side of one is the matching side of the other times the same number, the ratio. Angles do not change. If the sides are multiplied by k, the areas are multiplied by k².

Where this sits

Comes after
Proportions

Exercises from this rung

Generated by the app, from easiest to hardest

  1. On a 1:100 floor plan, a room is 6 cm long. How long is it really?

    • 6 m
    • 60 m
    • 600 m
    • 0.6 m

    Why 6 cm × 100 = 600 cm, which is 6 m.

    easier

  2. On a 1:50 floor plan, a room is 3 cm long. How long is it really?

    • 1.5 m
    • 150 m
    • 15 m
    • 0.15 m

    Why 3 cm × 50 = 150 cm, which is 1.5 m.

    in between

  3. Two similar shapes have a ratio of 4. If the small one's area is 8, what is the large one's area?

    Answer 128

    Why Each side is 4 times longer, and area has two dimensions: 8 × 4² = 8 × 16 = 128.

    harder