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You know that Area = base x height / 2, but what other ways are there to find the area of a triangle? Brace yourself for some potent formulae.

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In the above diagram, we are given two side lengths \[\rvert \overline{AB} \lvert = 3, \rvert \overline{AC} \lvert = 9.\] If \(\sin(\angle B+ \angle C) = \frac{1}{4},\) what is the area of \(\triangle ABC?\)

**Note:** The above diagram is not drawn to scale.

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In the above right triangle, if \[\angle ABC = 30^{\circ}, \angle ADC = 45^{\circ}, \lvert \overline{BC} \rvert = 14,\]
what is the area of \(\triangle ADC?\)

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