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
At first we must keep in mind that two triangles are similar when they have same angle configuration, that is, each pair of angles is congruent. If ABC and DEF, then and . Hence, and .