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Math Help - Find Area of ∆ABC

  1. #1
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    Find Area of ∆ABC

    If the area of square ABCD is 36, what is the area of
    ∆ABC which lies inside square ABCD?

    NOTE:

    Point Q(2,5) lies on CD of square ABCD.

    Point P(6,9) lies on BC on square ABCD.

    Point A of ∆ABC coincides with point A of square ABCD.

    I determined the area to be 21 but the text book tells me that the answer is 16.

    What did I do wrong?

    I hope this information is clearly stated here.

    Thanks

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  2. #2
    Super Member Matt Westwood's Avatar
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    Are you sure it's \triangle ABC you need to find the size of, not \triangle APQ?

    If so, we haven't got enough information about where A is, unless the square is positioned so the sides are horizontal and vertical.

    If this is the case, then C is at point (2, 9), which means A is at (8, 3) (6 over from C and 6 down - you know it's 6 because the square is area 36.

    So you need to find the area of the triangle (2,5), (6,9), (8,3).

    Can you take it from there?
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  3. #3
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    Yes..

    Quote Originally Posted by Matt Westwood View Post
    Are you sure it's \triangle ABC you need to find the size of, not \triangle APQ?

    If so, we haven't got enough information about where A is, unless the square is positioned so the sides are horizontal and vertical.

    If this is the case, then C is at point (2, 9), which means A is at (8, 3) (6 over from C and 6 down - you know it's 6 because the square is area 36.

    So you need to find the area of the triangle (2,5), (6,9), (8,3).

    Can you take it from there?

    Yes, I need to find the area of ∆APQ. Can you show me?
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  4. #4
    Super Member Matt Westwood's Avatar
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    Find the areas of the triangles you've got left and subtract those from the big square. They're easy right-angled triangles and should be no problem.
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