I would have thought this would be impossible without knowing the scalene triangle. To find the area of an equilateral triangle would be either using sin or Pythagoras. Let the triangle have sides a=b=c.

sine method:

Pythagoras:

Bisect the apex of the triangle so that it meets the base perpendicularly. The new base will then be

To find the height of the line we just drew (h) use Pythagoras' theorem:

.

We can then use this height in

Once you know a sideathen you can construct a scalene with the same area.