A triangle with side lengths in the ratio 3:4:5 is inscribed in a circle of radius 3.  What is the area of the triangle? Provide your answer as a decimal rounded to the nearest hundredth.
I know that a 3:4:5 triangle is a right triangle, so the hypotenuse must be the diameter of the circle. That means the hypotenuse has length 6, and the other two sides have lengths 3*6/5 = 3.6 and 4*6/5 = 4.8. To find the area of the triangle, I can use the formula A = (1/2)bh, where b and h are the lengths of the legs. So the area is A = (1/2)(3.6)(4.8) = 8.64. 