Question

find the area of a regular hexagon with radius length 4 cm. if necessary, write your answer in simplified radical form. area = \boxed{} cm²

Explanation:

Step1: Divide hexagon into triangles

A regular hexagon can be divided into 6 equilateral triangles, each with side length equal to the radius (4 cm).

Step2: Area of one equilateral triangle

The formula for the area of an equilateral triangle with side length \( s \) is \( \frac{\sqrt{3}}{4}s^2 \). For \( s = 4 \), area is \( \frac{\sqrt{3}}{4} \times 4^2 = 4\sqrt{3} \, \text{cm}^2 \).

Step3: Total area of hexagon

Multiply the area of one triangle by 6: \( 6 \times 4\sqrt{3} = 24\sqrt{3} \, \text{cm}^2 \).

Answer:

\( 24\sqrt{3} \)