Let P be the point (0,5), let Q be the point (6,9), and let R be the point (12,0). Determine the area of right-angled triangle PQR.
Let PQ be one leg and QR be the other leg
PQ = sqrt [ 6^2 + ( 9- 5)^2 ] = sqrt [ 36 + 4^2 ] = sqrt [52]
QR = sqrt [ (12 - 6)^2 + 9^2 ] = sqrt [ 6^2 + 9^2 ] = sqrt [ 117]
And the area of a right triangle = (1/2) (product of the leg lengths) =
(1/2)sqrt(52)sqrt(117) = (1/2) sqrt(6084) = (1/2) 78 = 39 units^2