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If ${m_1}$ and ${m_2}$ are the roots of equation $x^{2}+(\sqrt{3}+2)x+\sqrt{3}-1=0$ then area of the triangle formed by the lines $y={m_1}x, \: \: y={m_2}x, \: \: y=c$ is:

1. $\bigg(\dfrac{\sqrt{33}+\sqrt{11}}{4}\bigg) c^{2}$
2. $\bigg( \dfrac{\sqrt{32}+\sqrt{11}}{16}\bigg ) c$
3. $\bigg (\dfrac{\sqrt{33}+\sqrt{10}}{4} \bigg ) c^{2}$
4. $\bigg( \dfrac{\sqrt{33}+\sqrt{21}}{4} \bigg) c^{3}$

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