Roots , triangle and lines !!

The area of the triangle formed by the lines $y=m_1 \times x$ and $y=m_2 \times x$ and $y=c$ is $\frac{c^{2}}{a} \times (\sqrt{b}+\sqrt{d})$ ,where c is constant not given and $m_1$ & $m_2$ are the roots of the equation $x^{2} + (\sqrt{3} + 2)x + \sqrt{3}-1$ . Also a,b&d are integers ,what is the value of $a+b+d$ .