A regular hexagon with side length is inscribed in a circle. What is the area of the region inside the circle but outside the hexagon?

Answer and explanation

Correct answer: B.

  1. Step 1: For a regular hexagon the circumradius equals the side length, so and the circle's area is .
  2. Step 2: The hexagon is equilateral triangles of side , each of area .
  3. Step 3: The hexagon's area is , so the difference is .
Answer
.
Why not the others: and count only or triangles; doubles the triangle area.

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