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Math

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If two trapezoids have the same area, do they always have the same perimeter? Explain your thinking with words and diagrams.

  • Math -

    Go to en wikipedia
    and type: Trapezoid

    You can construct many trapezoides with some area but different perimeter.

    Area of trapezoid=((a+b)/2)*h

    Example:

    a+b=10 h=6 A=30

    a+b=2 h=30 A=30

    a+b=12 h=5 A=30

  • Math -

    No. You can construct many trapazoids with the same area with multiple side lengths, thus as perimeter is the addition of the outer side lengths of a figure, if two trapazoids have different side lengths but the same area, most of the time, the different side lengths will equal to different perimeters. Eg.

    Trapazoid 1:
    a=4 b=8 h=6
    A=(a+b)xh/2)
    =(4+8)x6/2)
    =12x6/2
    =72/2
    =36units squared

    side lengths=4 each
    P=(a+b+side length)x2
    =(4+8+4)x2
    =16x2
    =32units squared*

    Trapazoid 2:
    a=4 b=5 h=8
    A=(a+b)xh/2
    =(4+5)x8/2
    =9x8/2
    =72/2
    =36units squared

    side lengths=6&7
    P=a+b+6+7
    =4+5+6+7
    =22units squred*

  • Math -

    yes this is correct the answer is deez nutz

  • Math -

    If two trapezoids have the same area do they always have the same perimeter

  • Math -

    Umm I'm tryna figure that out but this web isn't really helpin moi

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