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2014 AMC 10A Problem 12

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2014 AMC 10A Problem 12AMC 10 Step by Step
Name:                             Date: September 13, 2026
Circles · difficulty 2 of 5 · about 3 min · position P11-15

A regular hexagon has side length 6. Congruent arcs with radius 3 are drawn with the center at each of the vertices, creating circular sectors as shown. The region inside the hexagon but outside the sectors is shaded as shown. What is the area of the shaded region?

figure

  1. A)

    273−9π27\sqrt{3}-9\pi

  2. B)

    273−6π27\sqrt{3}-6\pi

  3. C)

    543−18π54\sqrt{3}-18\pi

  4. D)

    543−12π54\sqrt{3}-12\pi

  5. E)

    1083−9π108\sqrt{3}-9\pi

Working