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

Answer 1

Draw a hexadecimal in a circle. Notice that from one corner to the other corner on the opposite side is equal to the diameter. Now connect all three opposite corners. Now we have 6 equilateral triangles. Each side of the triangle is the radius of the circle: 4.

Area of one of the triangles:

Base is 4, height is sqrt(4^2 - 2^2) = sqrt(12) = 2 sqrt(3)

Area of a triangle is 4*2*sqrt(3) / 2 = 4*sqrt(3)

We have 6 of these => 6*4*sqrt(3) = 24*sqrt(3)

Answer 2

Draw and label a diagram!

The hexagon is made up of 6 equilateral triangles. The sides are 4 m.

The angle between the sides is 60°

A = (4)(4)(sin 60º) / 2