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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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