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vovangra [49]
3 years ago
12

The angles of a quadrilateral measure 80, 100, 100 and 80 in the order. what kind of quadrilateral has this shape? How do you no

w?
Mathematics
1 answer:
Tanya [424]3 years ago
8 0
This quadrilateral would be a trapezoid. You have two obtuse angels next to each other, followed by two acute angels next to each other, in this case it's simply a matter of taking a pencil and drawing it out.
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Check the picture below.

now, we have a triangle with all three sides, thus we can use Heron's Area Formula on the triangle.

\bf \qquad \textit{Heron's area formula} \\\\ A=\sqrt{s(s-a)(s-b)(s-c)}\qquad \begin{cases} s=\frac{a+b+c}{2}\\[-0.5em] \hrulefill\\ a=10\\ b=26.695\\ c=22\\ s=29.3475 \end{cases} \\\\\\ A=\sqrt{29.3475(29.3475-10)(29.3475-26.695)(29.3475-22)} \\\\\\ A=\sqrt{29.3475(19.3475)(2.6525)(7.3475)}\implies A\approx \sqrt{11066.007} \\\\[-0.35em] \rule{34em}{0.25pt}\\\\ ~\hfill A\approx 105.195~\hfill

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