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:

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

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

$A=6\cdot\dfrac{a^2\sqrt3}{4}=\dfrac{3a^2\sqrt3}{2}$

We have a = 12cm. Substitute:

$A=\dfrac{3\cdot12^2\sqrt3}{2}=\dfrac{3\cdot144\sqrt3}{2}=3\cdot72\sqrt3=216\sqrt3\ cm^2$