smortandsons smortandsons
  • 03-02-2019
  • Mathematics
contestada

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

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gmany
gmany gmany
  • 03-02-2019

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]

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