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I have to construct all trapezoids $ABCD$ when the following are given: $a=8\ cm$, $c=3\ cm$, diagonal $|AC|= 6\ cm$, diagonal $|BD|= 7\ cm$. I have no idea how to write all the steps. Can someone help?

Thanks in advance.

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    do you mean $|AB|=8\;cm$ and $|CD|=3\;cm$ ? – 2017-02-27
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    Yes, that´s it. – 2017-02-27
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    What exactly do you mean by "construct" - I can see how to calculate all the lengths and angles using the laws of trigonometry. Is that what you want ? – 2017-02-27

2 Answers 2

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So we know that at least two sides of a trapezoid are paralell. This means that either AB and CD are paralell or BC and DA are paralell. So try to draw two trapezoids with either set of lines paralell and use sin and cos to find the different lengths of the sides.

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  1. Produce BA to X such that AX = 3.

  2. Construct the red circle centered at X with radius = 6.

  3. Construct the green circle centered at B with radius = 7.

  4. The two circles intersect at D. After joining, we have XD(= 6) and BD(= 7).

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