Area of a Hexagon

Date: 7/9/96 at 22:14:38
From: Anonymous
Subject: Area of a Hexagon

How do you calculate the area of a hexagon? 
Thanks for your help.

Date: 7/10/96 at 7:26:32
From: Doctor Anthony
Subject: Re: Area of a Hexagon

In the case of a regular hexagon the formula can be derived by 
thinking of six equilateral triangles meeting at a point. 

Let r = the side of the triangle; then the area of each triangle is 
(1/2)r^2*sin(pi/3) = (1/2)r^2*sqrt(3)/2 = (1/4)r^2*sqrt(3).

For six such triangles the area = (3/2)r^2*sqrt(3) 

-Doctor Anthony,  The Math Forum
 Check out our web site!  http://mathforum.org/dr.math/   

Date: 7/11/96 at 18:51:6
From: Anonymous
Subject: Area of a Hexagon

I've tried to work out the area of a hexagon with each side being 8 
feet.  I was working with the idea of 6 equilateral triangles. The 
answer I came up with was 96 sq.ft. Is this the right answer? Thanks 
for your help.

Date: 7/12/96 at 7:28:46
From: Doctor Anthony
Subject: Re: Area of a Hexagon

The area of one triangle is (1/2)*64*sin(60)

The area of six triangles is 3*64*sin(60) = 166.277 sq.ft

-Doctor Anthony,  The Math Forum
 Check out our web site!  http://mathforum.org/dr.math/