Christmas Maths

Santa (who for the purposes of this question can be modelled as an equilateral triangle) has an ornate belt buckle that he was given by Rudolph. 

For the purposes of this question, the buckle can be modelled as a point that is 3cm from one of Santa's vertices, 4cm from the second and 5cm from the third (Santa is being modelled as quite a small equilateral triangle).

What is Santa's area?

Solution