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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.

Which of the following triangles has a larger area:

Triangle A, with side lengths of \( 13, 13, 10 \)

\[\text{or } \]

Triangle B, with side lengths of \( 13, 13, 24 \)?

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In a square \(ABCD\), \(E\) and \(F\) are the midpoints of sides \(AB\) and \(AD\), respectively. A point \(G\) is taken on segment \(CF\) in such a way that \(2CG=3FG\).

If the side of the square is \(2\), then what is the area of \(\triangle{BEG}\)?

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Find the area of a triangle with sides \(\sqrt{13}, \sqrt{61} , \sqrt{80} \).

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