Question

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

Answer 1

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:

$A_\triangle=\dfrac{a^2\sqrt3}{4}$

Substitute a = 20 cm:

$A_\triangle=\dfrac{20^2\sqrt3}{4}=\dfrac{400\sqrt3}{4}=100\sqrt3\ cm^2$

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

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