Geometry – Circle Area

April 28, 2016 at 12:29 am 2 comments

Illustrated below is a quarter-circle, containing two semicircles of smaller circles. Prove that the red segment has the same area as the blue.

Why does red = blue?

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Entry filed under: Uncategorized.

⚡Presentation ‘Math Groups Now What? Josh Holt, Principal Catherine Castillo, Numeracy Coach Portland Elementary.’ Why Not to Trust Statistics

2 Comments Add your own

  • 1. M  |  July 15, 2016 at 2:22 pm

    Red = All – 2 * SmallHalf + Blue

    All = 1/4 * 2 * PI * R^2

    SmallHalf =1/2 * 2 * PI *(1/2 * R)^2

    -> Red = (1/4 * 2 * PI * R^2) – 2 * (1/2 * 2 * PI *(1/2 * R)^2) + Blue
    Red = 1/2 * PI * R^2 – 2 * 1/4 *PI *R^2 + Blue
    Red = PI * R * (1/2 – 2/4) + Blue
    Red = Blue
    Q.E.D.

  • 2. squarepi  |  July 15, 2016 at 2:36 pm

    Thanks for stopping by. This was a cool problem that I’m hoping to share with my students.

    Solid solution too!

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