Aregular hexagon has a radius of 20 in. what is the approximate area of the hexagon

Remark

You need 2 facts to solve this 

1.   The area of a hexagon is 

     A = 3*(sqrt(3) ) * a^2/2 

     Just to make this clear, I'll put it in Latex

2. The second fact you need to know is that the radius = the length of the side a.

Givens

r = 20 in

a = r where a is the length of the side of a hexagon.

Formula Substitute and solve.

A = 3*(sqrt(3) * a^2 ) / 2

A = 3*(sqrt(3) * 20^2) / 2

A = 3*sqrt(3) * 400 / 2

A = 3*sqrt(3) * 200

A = 3*1.7321 * 200

A = 1039 square inches.

step-by-step explanation:

given that there are two triangles j'k'l' and jkl>

the former is got by dilating the second one.

when drawn on a grid, (graph paper) coordinates of vertices of first triangle is

(6,12)j, (9,6)k and (12,9)l

side jk has length = distance between j and k

=

side j'k'=distance between j' and k'

=

ie j'k'l' has sides 1/3 of that of corresponding sides of jkl.

hence scale factor of 1/3 is used to get j'k'l'from jkl