We look for the distance between each one of the vertices applying the following formula: d = root ((x2-x1) ^ 2 + (y2-y1) ^ 2) For QR: QR = root ((4-6) ^ 2 + (-7 + 2) ^ 2) QR = 5.385164807 For QS: QS = root ((2-6) ^ 2 + (-5 + 2) ^ 2) QS = 5 For RS: RS = root ((2-4) ^ 2 + (-5 + 7) ^ 2) RS = 2.828427125 Now we apply the heron formula: A = root (s * (s-a) * (s-b) * (s-c)) Where, s = (a + b + c) / 2 s = (5.385164807 + 5 + 2.828427125) / 2 s = 6.606795966 Substituting: A = root (6.606795966 * (6.606795966-5.385164807) * (6.606795966-5) * (6.606795966-2.828427125)) A = 7.00000000 A = 7 units ^ 2 Answer: The area, in square units, of triangle QRS is: A = 7 units ^ 2
