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Given trapezoid ABCD with $\angle AOB = 60°$, $AD = 3$ cm, $BC = 8$ cm, $MN (midline) = 8.5$ cm.

Find $AB$, $DC$ (the bases) and the area of the trapezoid $S$.

enter image description here

There are two formulas that I could use to find the area of the trapezoid. Since we already have the midline, I will probably have to use the second formula below, which means I need to find the height.

$S = \frac{(AB + CD) \times h}{2}$ or $S = MN \times h$ => $MN = \frac{AB + DC}{2}$

I wish I could add more to the question related to what I've tried, but I really have no idea where to start from.

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  • $\begingroup$ They should probably be named M and N, but that’s by definition $\endgroup$
    – nop
    Commented Mar 4, 2022 at 15:55
  • $\begingroup$ @Intelligentipauca, my drawing was horrible. It's better rn. $\endgroup$
    – nop
    Commented Mar 4, 2022 at 16:05
  • $\begingroup$ Can you use trig? $\endgroup$
    – Vasili
    Commented Mar 4, 2022 at 16:21
  • $\begingroup$ @Vasya everything should be possible as soon as it solves it. $\endgroup$
    – nop
    Commented Mar 4, 2022 at 16:42

1 Answer 1

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Comment: the given value for angle AOB is wrong . the correct value is $135^o$, only with this value the figure can be constructed. In this case:

$AB=123.69$

$DC=46.31$

$altitude=29.83$

To moderator: I can not comment and I can not attach figure. I do not know what is wrong ? Is it due to site? Please guide.The top titles are vanished.And every time I want to post my answer the site ask me for human verification.

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