In the given figure, ABCD is a quadrilateral in which AC = 24 cm,

Area of quadrilateral $\mathrm{ABCD}=\left(\begin{array}{ll}\text { Area of } \Delta \mathrm{ADC} \\ \text { tarea of } \Delta \mathrm{ACB}\end{array}\right)$

$=\left(\frac{1}{2} \times \mathrm{AC} \times \mathrm{DM}\right)+\left(\frac{1}{2} \times \mathrm{AC} \times \mathrm{BL}\right)$

$=\left[\left(\frac{1}{2} \times 24 \times 7\right)+\left(\frac{1}{2} \times 24 \times 8\right)\right] \mathrm{cm}^{2}$

$=(84+96) \mathrm{cm}^{2}$

$=180 \mathrm{~cm}^{2}$

Hence, the area of the quadrilateral is $180 \mathrm{~cm}^{2}$.