The area of a regular hexagon is 35in squared.

Question

Find the length of a side.

Answer 1

Given that area of a regular 35 in squared

The hexagon consists of 6 triangles

The triangles are also isosceles, so their base angles are each 60. Thus they are equilateral, ie they have equal side

where L is the length of any side

From formula

(1/2) AO * BO * sin60

=(1/2)L^2.(√3/2)                  (The value of sin60 = √3/2)

= (√3/4).L^2

So the area of the hexagon =( 6 * area of any triangle)

= (3√3/2).L^2

 

But the area of the hexogan is given as 35 in squared

 

(3√3/2).L^2 =35

 

L^2 =70/(3√3)

 

L^2 = 13.4715

 

L = 3.67 inches.