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April 30th, 2012, 03:48 AM   #1
lei
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Finding altitude of a part of trapezoid with given area...

Is there a formula for this one?

Please help
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April 30th, 2012, 03:58 AM   #2
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Re: Finding altitude of a part of trapezoid with given area.

Extend to right to form right triangle.
Then work with similar right triangles.
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April 30th, 2012, 01:01 PM   #3
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Re: Finding altitude of a part of trapezoid with given area.

y = ax + b.

When x = 0, y = 10, when x = 10, y = 5. Plug into equation and solve for a and b.
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April 30th, 2012, 07:13 PM   #4
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Re: Finding altitude of a part of trapezoid with given area.

Area of a trapezoid , where is height and and are the parallel sides. So we've got



as the area of the blue part and



as area of the red part, where is the width of the blue area and is the length of the segment between the blue and red areas.

From the first equation,



Substitute that into the second equation,

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May 1st, 2012, 03:57 AM   #5
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Re: Finding altitude of a part of trapezoid with given area.

Extending to form right triangle: triangle has legs 10 and 20; total area 100; new red area = 100-23 = 77:
so y(20 - x) = 154 [1]

Similar right triangles means y / (20 - x) = 10/20:
so x = 20 - 2y [2]

[2] in [1]: y[20 - (20 - 2y)] = 154; solve: y = SQRT(77)
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