Question

What is the area of a regular hexagon with a side length of 12 cm
With process please

Answer 1

Look at the picture.

The area of the hexagon is equal six times the area of the equilateral triangle.

The formula of the equilateral triangle with the leg a:


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

Therefore the formula of the area of the hexagon with a side lenght a is:


`A=6\cdot(a^2\sqrt3)/(4)=(3a^2\sqrt3)/(2)`

We have a = 12cm. Substitute:


`A=(3\cdot12^2\sqrt3)/(2)=(3\cdot144\sqrt3)/(2)=3\cdot72\sqrt3=216\sqrt3\ cm^2`