This cant be Heron's formula
Geometry
Level
3
A scalene obtuse triangle with integer side lengths and an area of 6 sq units has three medians with lengths of a b and c. Find the area of a triangle with side lengths a, b, and c.
15/2
9
3
9/2
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The triangle formed by the medians of a given triangle will have an area three-fourths the area of the given triangle.
If ABC is a triangle with medians of lengths u, v, and w, and CGF is a triangle with sides the same length as these medians then the ratio of the area of triangle ABC to the area of triangle CGF is 4 to 3.
The triangle CGF can be constructed by making segment FG parallel and congruent to median BE and segment CG parallel and congruent to median AD. The ratio of the areas can be proved in several ways, but suffice to see triangle AFC is half the area of ABC, triangle CHF is half the area of triangle CGF, and triangle AHF is one fourth the area of triangle AFC.
Therefore the ratio of the areas of triangle AFC to FHC is 4 to 3 and so the ratio of the area of triangle ABC to CGF is 4 to 3.
Next step. Use Heron's formula for the area of the triangle with sides of length u, v, and w.
The area of the triangle with medians of length u, v, and w is given by this formula:
So the required area is (6*3)/4 = 9/2