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Area of a triangle from the coordinates of its vertices

This type of question, asked 4 times: 2 May 2023 S2, 11 May 2023 S1, 12 May 2024 S1, 11 Apr 2026 S1. All 4 questions below, oldest first.

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  1. Question 1

    2 May 2023 S2

    128
    The area of the triangle whose vertices are A(1,−1,2)A(1,-1,2), B(2,1,−1)B(2,1,-1) and C(3,−1,2)C(3,-1,2) is

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  2. Question 2

    11 May 2023 S1

    136
    The area of the triangle with vertices (1,2,0), (1,0,2) and (0,3,1) is

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  3. Question 3

    12 May 2024 S1

    112
    If the area of the triangle with vertices (1,2,0)(1,2,0), (1,0,2)(1,0,2) and (0,x,1)(0,x,1) is 6\sqrt{6} square units, then the value of xx is

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  4. Question 4

    11 Apr 2026 S1

    91
    Let A(2,3,0),B(0,3,2)A(2, 3, 0), B(0, 3, 2) and C(4,0,3)C(4, 0, 3) be vertices of a triangle, then the area of the triangle is

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