Mathematics

Question

A regular hexagon has sides of length 6cm. Find the perpendicular distance between two opposite faces.

Answer 1

The internal angles of a regular hexagon is 360/6 = 60 degrees

 

the diagonals connecting the two edges of opposite sides makes equilateral triangles with apex at the centre.

 

Hence the perpendicular distance would be twice that of the longer side of a 30/60/90 degree triangle with hypothenuse 6 cm

 

Using Pythagoras theorem d = 2* (6² - 3²)^1/2

 

Hence this length would be 2*3(3)^1/2  = 6(3)^1/2  = 10.39 cm