Correct yes, GPT also yes. Why do you bother with all of the unecessary information when you can just use heron's directly?
"To find the area of triangle PQR, we need to calculate the lengths of PX and YQ.
Using the Pythagorean theorem, we can calculate the length of PX:
PX^2 = PR^2 - PQ^2 = 1296 - 1296 = 0
PX = 0
Using the Law of Cosines, we can calculate the length of YQ:
YQ^2 = QR^2 + MY^2 - 2*QR*MY*cos(QPR)
YQ^2 = 256 + 2500 - 2*16*50*cos(QPR)
YQ^2 = 2808
YQ = 53.08"
Also I'm pretty sure PX isn't zero. This is also how GPT writes math. You never use YQ or PX later, another sign of GPT.