Question

A regular hexagon is formed by six equilateral triangles this makes it somewhat easy to find the area of the hexagon using the properties 30-60-90 right triangles.

Use the diagram to solve for the area of a hexagon with sides equal to 4cm.

If the side length is 4cm what is half of the side length? ___

Use what you know about 30-60-90 triangles to give the length of the APOTHEM (this is the green solid line shown in the diagram that goes from the center of a polygon to the midpoint of a side.)

Calculate the area of the complete hexagon and show your steps clearly:

Answer 1

1/2 of the side length p= 1/2 x 4 =2
centre angle=360/6=60 degrees

The APOTHEM bisects or divides the centre angle into two equal angles
1/2 of the centre angle=60/2=30 degrees
tan 30 degrees = 2/APOTHEM
APOTHEM=2/tan 30= 3.46 cm

The APOTHEM is the perpendicular height of the equilateral triangle given in the diagram.
Area of the equilateral triangle
=1/2 x 4 x 3.46
=6.93 cm^2
Area of the regular hexagon= 6 x area of the equilateral triangle= 6 x 6.93 =41.6 cm^2

Hope this helps!