This is an IGCSE probability question that is giving me a lot of trouble. Since it's not just a probability problem and that the non probability part is the part giving me trouble I decided to put it here.

A dartboard is in the shape of an equilateral triangle inside which is inscribed a circle.

A dart is randomly thrown at the board (Assume that it hits the board).

A) Given that tan 60 degrees = \sqrt{3} and sin 60 degrees =

\sqrt{3} /2

show that the probability of the dart hitting the board inside the circle is

\pi /3 \sqrt{3}

The diagram given looks like this: http://tinyurl.com/3nym92q

My working:

The probability should be the area of the circle (\pi r^2) over the area of the triangle(half* unknown base * unknown height)

So you should somehow end up with \pi r^2/ 3r^2 \sqrt{3} which simplifies down to \pi /3 \sqrt{3}

But how do use the information in the question to find out that the area of the triangle is 3r^2\sqrt{3} ?