ABC is an equilateral triangle. Let P be any point inside it such that PA=3 PB=5 PC=4 Then find area of he triangle ABC?

you will have to rotate the triangle 60 deg about one of its vertices and then note a 60 deg angle. apply cosine rule and finally obtain a^2= 25+12root3

hence area= root3 * a^2/4

actually this is a tricky question and wont be asked in any exam. the solution to this is easily available on google search as well. it has a long history behind it and is also a ‘coffin’ problem asked in the early 90s to discriminate against the black kids.