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Math Help - Trapezoid Altitude

  1. #1
    lei
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    Trapezoid Altitude

    Is there a formula to calculate the altitude of a part of a trapezoid?

    Please see the attachment.

    I would like to solve for X

    Thanks,
    Attached Thumbnails Attached Thumbnails Trapezoid Altitude-trapezoid.jpg  
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  2. #2
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    Re: Trapezoid Altitude

    Quote Originally Posted by lei View Post
    Is there a formula to calculate the altitude of a part of a trapezoid?
    I would like to solve for X
    This can be done. But it is messy.
    Let r be the longer base of the red trapezoid.
    The using area of the red trapezoid, you can get r in terms of x
    Then use the area of the blue trapezoid to solve for x.
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    Re: Trapezoid Altitude

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  4. #4
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    Re: Trapezoid Altitude

    Quote Originally Posted by lei View Post
    Is there a formula to calculate the altitude of a part of a trapezoid?

    Please see the attachment.

    I would like to solve for X

    Thanks,
    1. Use a coordinate system. Then the smaller parallel of the blue trapezoid is calculated by:

    p = 10-\frac12 x

    2. The area of the blue trapezoid is calculated cosequently:

    A = \frac{10+10-\frac12x}2 \cdot x = 23~\implies~10x-\frac14 x^2 = 23

    3. This is a quadratic where x must be between zero and 10. Solve for x.

    4. I've got x=20-\sqrt{308}
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