Question

Help? find the area of the regular polygon round to the nearest tenth.

Answer 1

`A=779.4\ cm^(2)`

Explanation:

we know that

The area of a regular hexagon is equal to the area of six equilateral triangles

Applying the law of sines

The area of six equilateral triangles is equal

`A=6[(1)/(2)b^(2)sin(60)]`

where

b is the side length of the regular hexagon

we have

`b=10√(3)\ cm`

`sin(60\°)=√(3)/2\ cm`

substitute

`A=6[(1)/(2)(10√(3))^(2)(√(3)/2)]`

`A=450√(3)=779.4\ cm^(2)`