Question

What is the area of a regular hexagon with an apothem of 7?

Answer 1

`98sqrt(3)`

Explanation:

The radius of the hexagon is `2/(sqrt(3)` times the apothem since it forms the hypotenuse of a right angled triangle with sides in ratio `1:sqrt(3):2`

The area of one of the `6` equilateral triangles that make up the hexagon is:

`1/2 xx "base" xx "height" = 1/2 xx "radius" xx "apothem"`

`=1/2 xx 2/sqrt(3) xx "apothem" xx "apothem"`

`=1/2 xx 2/sqrt(3) xx 7 xx 7 = 49/sqrt(3) = (49sqrt(3))/3`

The area of the hexagon is `6` times this:

`6 xx (49sqrt(3))/3 = 98sqrt(3)`