Hello, rcmango!

FInd the area of the triangle whose verices are: P(1,1,-1), Q(1,-1,1), R(-1,1,1)

The "symmetry" of the coordinates made me suspicious. . ._

I found the lengths of the sides to be: PQ = QR = RP = 2√2

. . It's an equilateral triangle!

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . _

The area of an equilateral triangle of sidexis: .A .= .(√3/4)x²

. . . . . . . . . . . . . . . . _ . . . . _ . . - - . ._

Therefore: .Area .= .(√3/4)(2√2)² .= .2√3