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2005 AMC 10A Problem 12

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2005 AMC 10A Problem 12AMC 10 Step by Step
Name:                             Date: September 13, 2026
Circles · difficulty 3 of 5 · about 4 min · position P11-15

The figure shown is called a trefoil and is constructed by drawing circular sectors about sides of the congruent equilateral triangles. What is the area of a trefoil whose horizontal base has length 22 ?

figure

  1. A)

    13π+32\frac{1}{3}\pi+\frac{\sqrt{3}}{2}

  2. B)

    23π\frac{2}{3}\pi

  3. C)

    23π+34\frac{2}{3}\pi+\frac{\sqrt{3}}{4}

  4. D)

    23π+33\frac{2}{3}\pi+\frac{\sqrt{3}}{3}

  5. E)

    23π+32\frac{2}{3}\pi+\frac{\sqrt{3}}{2}

Working