Question

Find the area of a regular hexagon with a perimeter of 12cm.

Answer 1

`6√(3)`
`cm^(2)`

Explanation:

Here is a fact to remember. A hexagon is always made up of 6 equilateral triangles.

So if the perimeter of the Hexagon is 12 cm, then each side is 2 cm.

The area of an equilateral triangle is
`(s^(2)√(3) )/(4)`.

So plugging in 2 gets us the area of one triangle.

s = 2

`2^(2)√(3)/4 = \sqrt3`

The area of 6 triangles will be
`6√(3)`
`cm^(2)`.