Answer:
A = 600√3 cm²
Step-by-step explanation:
Diagonals divide a regular hexagon into six equilateral triangles (look at the picture).
The formula of an area of an equilateral triangle with side a:
[tex]A_\triangle=\dfrac{a^2\sqrt3}{4}[/tex]
Substitute a = 20 cm:
[tex]A_\triangle=\dfrac{20^2\sqrt3}{4}=\dfrac{400\sqrt3}{4}=100\sqrt3\ cm^2[/tex]
The area of a regular hexagon is equal six times the area of a triangle:
[tex]A=6\cdot100\sqrt3\ cm^2=600\sqrt3\ cm^12[/tex]
