Find the area of the regular polygon...
Uh how?

16sqrt(3) units²

Step-by-step explanation:

This shape consists of 6 congruent triangles

Each angle = (6-2)×180/6 = 120

These are 6 equilateral triangles

6(½ × 8 × 8 × sin(60)) = 16sqrt(3) units²

Answer is Area= 166.08^2

Hexagon has 6 sides

Lets focus on 1 and say the height is 8 as they look like equilateral triangles.

We cna work out shaded areas of 1/2 a triangle later to find height.

Base 1 = 8 / 2   = 4

Step-by-step explanation:

The altitude, divides the equilateral triangle into two 30^-60^-90^30∘−60∘−90∘ right triangles and divides the bottom side in half.  

In a 30∘−60∘−90∘ right triangle, the sides of the triangle equal x, x3–√, and 2x. In these equations x equals the length of the smallest side, which in our triangle is s2 or 3–√2  = 3/2

Therefore h = x square of 3

therefore x = square 3 / 2

therefore h = square 3/ 2  x  square 3/1 = 3/2

Therefore Height = 3/2 = 3.46

To find area we 1/2 base  x height

= 4 x 3.46 = 13.84 for one shaded half triangle.

12 shaded from 6 = 13.84 x 12=166.08^2