Question

Please help me out please

Answer 1

Answer:

the area of the hexagon is approx. 187.1 in²

Step-by-step explanation:

Picture this regular polygon as being a hexagon made up of six equilateral triangles of side 12 in.  We find the area of one such triangle and then multiply that by 6 to obtain the total area of the hexagon.

One such equilateral triangle has three sides all of length 12 in, and all the interior angles are 60°.  The height of one such triangle is

h = (12 in)sin 60°, or

                  √3

h = (12 in) -------- = 6√3 in

                     2

So, with base 12 in and height 6√3 in, the area of one such equilateral triangle is

A = (1/2)(12 in)(6√3 in) = 36√3 in²

and the total area of the hexagon is 6(36)√3 in², or approx. 187.1 in²