Geometry
# Area of Triangles

$\rvert \overline{AB} \lvert = 3, \rvert \overline{AC} \lvert = 9.$ If $\sin(\angle B+ \angle C) = \frac{1}{4},$ what is the area of $\triangle ABC?$

In the above diagram, we are given two side lengths**Note:** The above diagram is not drawn to scale.

$\angle ABC = 30^{\circ}, \angle ADC = 45^{\circ}, \lvert \overline{BC} \rvert = 14,$ what is the area of $\triangle ADC?$

In the above right triangle, if