Question

A circle is inscribed in a regular hexagon. The hexagon has a perimeter of 18 radical 3. G is the center of the polygon and the center of the circle.
a. Find the radius of the circle.
b. Find the radius of the hexagon. (The radius of a polygon is the segment that joins the center of the polygon with a vertex.)
c. Find the area of the hexagon.
Express your answers as either a reduced fraction or a radical in simplest form. (Not a decimal).
Help me with this please!

Answer 1

A Hexagon has 6 sides. The perimeter was given meaning it is the sum of all the sides. Take note that each side has equal length

If you know how long one side is, you can use this formula
r= a sqrt(3)/2 where a= one side of the hexagon, to find the radius of the circle

YOu can also find the radius of the hexagon if you know the length of one side.
s= length of one side
(s)/2sin(180/n)

For the area
s^2N/4tan(180/n)

n= number of sides
s= length of one side