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## Area of Triangles

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.

# Level 2

Which of the following triangles has a larger area:

• triangle A with side lengths $$13, 13, 10$$, or
• triangle B with side lengths $$13, 13, 24\, ?$$

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 $$\triangle{BEG}$$?

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

In triangle $$\triangle ABC$$, $$BE$$ and $$CF$$ are medians. $$BE=9\text{ cm}$$, $$CF=12\text{ cm}$$. If $$BE$$ is perpendicular to $$CF$$, find the area of the triangle $$\triangle ABC$$ in $$\text{ cm}^2$$.

$$ABCD$$ is a parallelogram. The area of $$ABCT$$ is 45 and $$T$$ is the midpoint of $$AD$$. Find the area of triangle $$ACD$$.

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