To find the length of the diagonals, Troy should use the Pythagorean Theorem. The diagonal is going to be the hypotenuse of the triangle (the side directly across from the 90 degree angle).
a^2 + b^2 = c^2
6^2 + 10 ^2 = c^2
136 = c^2; find the square root of 136
c = 11.66 feet
Troy's diagonals are approximately 11.66 feet.