Area of a hexagon?

Question

How do you find an area of a regular hexagon when one of it's sides is 4?

Answer 1

split it up into triangles by connecting the opposite corners, and then because all sides are the same you only have to find one of them and multiply it by 6

Answer 2

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)

Answer 3

Divide the hexagon into small triangles and you will be able to solve the problem.
1. Hexagonal will be 6 triangle with one angle equal to 360/6 = 60 degree.
2. Two sides of the triangle are same so we know that when two sides are same then the angles are same as well.
3. All the angles are 60 degree and you know the length of one side i.e 4.
4. Find area of triangel by first finding the height using cos theta or sign theta and then multiply the area by 6 to get complete area

http://www.mathreference.com/geo,hex.html

Answer 4

The equation for area of a regular hexagon is ((3√3)/2)*L² or (3L²*√3)/2 where L is the length of a side.

L = 4
(3L²*√3)/2 = (3(4)²*√3)/2
= (3*16*√3)/2
= (48√3)/2
= 24√3
= approximately 41.6

If you want to know how to derive that equation, see this site:
http://www.mathreference.com/geo,hex.html

Answer 5

for any regular polygon
A=(1/4)ns^2(cos(pi/n)/sin(pi/n) where n is the # of sides & s is the length of a side
for a hexagon
A=(1/4)6*4^2/tan(pi/6)=24/(√3)/3=24√3=41.57

You could also get this by dividing the hexagon into 6 equilateral triangles with side=4
the hight of each is 4√3/2=2√3 so (1/2)*6*4*2√3=24√3=41.57

Answer 6

You need the distance from the center to the midpoint of a side (the apothem). Find this by drawing it, and using Pythagorean theorem. (The distance from the center to a vertex is 4, just like the sides.)

The formula for area of a regular polygon is A = 1/2 a p
where a = length of apothem and p = perimeter.

Hope that helps; you can IM if you want more info.

Answer 7

Area = (3 * sqrt(3) * x^2) / 2
where x is the length of a side of the hexagon
eg if x = 4
Area = (3 * sqrt(3) * 16) / 2
= 24 * sqrt(3)
Or, approximated:
Area = 2.598 * x^2
=41.57

Answer 8

a regular hex is 6 equilateral triangles ( 360 / 6) = 60 degree
the base is 4
height = 2*root(3) ( 30,60,90 tri... the height is root(3) * base)

one half base times height times 6
.5 (4) (2 root(3)) * 6 = (24 * root(3) ) ....aprox 41.5692 sq units

Answer 9

I believe it would be the equivalent of 6 equilateral triangles of base 4. Try figuring that out.