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2020 AMC 10B Problem 14

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2020 AMC 10B Problem 14AMC 10 Step by Step
Name:                             Date: September 13, 2026
Circles · difficulty 3 of 5 · about 5 min · position P11-15

As shown in the figure below, six semicircles lie in the interior of a regular hexagon with side length 2 so that the diameters of the semicircles coincide with the sides of the hexagon. What is the area of the shaded region — inside the hexagon but outside all of the semicircles?

figure

  1. A)

    63−3π6\sqrt{3}-3\pi

  2. B)

    932−2π\frac{9\sqrt{3}}{2} - 2\pi

  3. C)

    332−π3\frac{3\sqrt{3}}{2} - \frac{\pi}{3}

  4. D)

    33−π3\sqrt{3} - \pi

  5. E)

    932−π\frac{9\sqrt{3}}{2} - \pi

Working