If the apothem of a reg. hexagon is 4.5 cm,how long is each side of the hexagon? Can you explain how u got it?

Answer 1

Sure, the correct answer is 5.2 cm

For a regular hexagon the length of a side, S, is related to the length of the apothem, A, by:

S = 2A / sqrt(3) = 2A cot(60) = 2A tan(30)

So if A = 4.5cm, then S = 9/sqrt(3) = 5.196...or about 5.2cm

To see how to get it:

Imagine six line segments, R, drawn radially from the centre of the hexagon to the 6 vertices (where 2 sides of the hexagon meet) forming 6 equilateral triangles. Every angle is 60 degrees. Now, the apothem goes from the centre of the hexagon to the midpoint of a side S. It therefore bisects the 60 degree central angle and forms a right triangle, with the length of one side being S/2, and the apothem A being the length of the 2nd side.(Note: the hypotenuese = R). So we must have S/2 divided by A equal to tan(30). So S = 2A tan(30) = 2A x 0.57735. If A = 4.5cm, then S = 9 x 0.55735 = 5.2cm

Here's a couple of useful links

http://mathworld.wolfram.com/Hexagon.html

http://mathworld.wolfram.com/Apothem.html

Answer 2

A regular hexagon has all sides equal and equal to the radius of the circle it can be inscribed in (because 360/6 sides = 60)

So what you are talking about is an equilateral triangle with height =4.5

Using Pythagora x^2 + x^2/4 = 4.5^2
So x^2 = 20.75 *4/5
x = 4 approximately

Answer 3

what's an apothem?? if ur talking about the sides well...... a hexagon has 6 sides right? then just divide 4.5 by 6 and you get 0.75... what's an apothem anyway?

Answer 4

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