Question

Find the area of the regular hexagon if a side is 20 cm.

Answer 1

A = 600√3 cm²

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:

`A_\triangle=(a^2\sqrt3)/(4)`

Substitute a = 20 cm:

`A_\triangle=(20^2\sqrt3)/(4)=(400\sqrt3)/(4)=100\sqrt3\ cm^2`

The area of a regular hexagon is equal six times the area of a triangle:

`A=6\cdot100\sqrt3\ cm^2=600\sqrt3\ cm^12`