A regular hexagon is inscribed in a circle of radius 4 meters. What is the area of the hexagon?

Question

Here is the link to the figure that is provided.

https://docs.google.com/document/d/1tJhAZPM7OazfC0jWa8owkAx9Ft0njT9VXBpfiK8foyc/edit?usp=sharing

Answer 1

If you have a radius of 4 that means you are drawing a line from any of the vertices of the hexagon into the middle. A hexagon makes 6 equilateral triangles within the shape. So, essentially each individual side of the triangles within the hexagon all have the same length, which would be 4 meters here. A formula to find the area of a hexagon is

Area= (3√3÷2) × r² r = the length of 1 side (4 meters)

3√3 = 5.196 → 5.196/2 = 2.598 → 2.598 × 4² = 41.57 meters²