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Math Help - Construction I

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    Construction I

    Given a convex quadrilateral, construct a triangle whose area is the same as the area of the quadrilateral.
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  2. #2
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    Quote Originally Posted by MATNTRNG View Post
    Given a convex quadrilateral, construct a triangle whose area is the same as the area of the quadrilateral.
    Well, if you know the quadrilateral's area, simply construct a right triangle
    where the legs are a and b, such that ab/2 = quad's area
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  3. #3
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    Quote Originally Posted by MATNTRNG View Post
    Given (where?) a convex quadrilateral, construct a triangle whose area is the same as the area of the quadrilateral.
    1. Draw a diagonal BD. Produce the side AB.

    2. A parallel to BD through C crosses the line (AB) in C'. The triangle BDC' has the same area as triangle BDC.

    3. Thus triangle AC'D has the same area as the quadrilateral ABCD.
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