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      Question

      The vertices of a triangle are given as (5, 4), (9, 6),

      and (1, 5). Determine the area enclosed by this triangle.
      A 6 square units Correct Answer Incorrect Answer
      B 8 square units Correct Answer Incorrect Answer
      C 9 square units Correct Answer Incorrect Answer
      D 4 square units Correct Answer Incorrect Answer

      Solution

      Area of a triangle whose vertices are (x1,y1) , (x2,y2) and (x3,y3) : = (1/2) X |x1(y2 - y3) + x2(y3 - y1) + x3(y1 - y2) | Here, 'x1' = 5, 'x2' = 9, 'x3' = 1, 'y1' = 4, 'y2' = 6 and 'y3' = 5 Required area = (1/2) X |5 X (6 - 5) + 9 X (5 - 4) + 1 X (4 - 6) | = (1/2) X | 5 + 9 - 2| = (1/2) X 12 = 6 square units

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