The Three Medians

There's a formula to find the area of a triangle given 3 medians: $\frac { 4 }{ 3 } \sqrt { { s }_{ m }({ s }_{ m }-{ m }_{ 1 })({ { s }_{ m } }-{ m }_{ 2 })({ s }_{ m }-{ m }_{ 3 }) }$

Where ${ m }_{ 1 },{ m }_{ 2 },{ m }_{ 3 }$ are the medians and ${ s }_{ m }=\frac { { m }_{ 1 }+{ m }_{ 2 }+{ m }_{ 3 } }{ 2 }$

Cross reference: https://brilliant.org/problems/triangle-of-medians/

It can be shown that

1. Medians of a triangle can be moved parallel to themselves to form a closed loop i.e. a triangle.

2. The area of such a triangle is 3/4 the area of the original triangle

From Heron's formula, area of the 'median triangle' is 24

Thus the area of the original triangle must be $24 \times \frac{4}{3} = 32$