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Grade 7

Half of the leftover

Two equal circles fill a 24 by 12 cm rectangle and a diagonal runs corner to corner through the point where they touch. The shaded scraps look unrelated -- a half-turn shows they are exactly half of everything the circles leave behind.

  1. 1

    Shaded area

    rr24 cm12 cm
    A 24 cm by 12 cm rectangle holds two equal circles side by side. Each circle touches the top edge, the bottom edge and one end of the rectangle, and the two circles touch each other at the centre. A diagonal runs from the bottom-left corner to the top-right corner, passing through the point where the circles touch. The parts of the rectangle that lie outside the circles and below the diagonal are shaded. What is the shaded area?