o is the center of the regular hexagon below. find its area. round to the nearest tenth if necessary.

Answer:

$10.4$

Explanation:

Step1: Divide hexagon into triangles

A regular hexagon can be divided into 6 equilateral triangles with side - length equal to the radius of the circum - circle. Here the radius (r = 2), so the side - length of each equilateral triangle (a=2).

Step2: Find area of one equilateral triangle

The area formula for an equilateral triangle is (A_{\triangle}=\frac{\sqrt{3}}{4}a^{2}). Substitute (a = 2) into the formula: (A_{\triangle}=\frac{\sqrt{3}}{4}\times2^{2}=\sqrt{3}).

Step3: Find area of hexagon

Since the hexagon is composed of 6 such equilateral triangles, (A = 6A_{\triangle}). So (A=6\times\sqrt{3}\approx6\times1.732 = 10.392\approx10.4).