Question

The regular hexagon has a radius of 4 in.

A regular hexagon has a radius of 4 inches.

What is the approximate area of the hexagon?

24 in.2
42 in.2
48 in.2
84 in.

Answer 1

For a regular hexagon the side equals the radius, so s = 4. Split the hexagon into 6 equilateral triangles; each has area (√3/4)s^2 = (√3/4)(16) = 4√3. Total area = 6·4√3 = 24√3 ≈ 41.6 in^2, so the closest choice is 42 in.^2.