If you extend two of the lines until they meet, as shown, and then also draw a line from this new point to the point inside the hexagon you will form two new triangles with the same base and height as two of the given triangles. The sum of these, and therefore the area of the quadrilateral, will be 12. But this 12 is also the sum of the other given triangle and the new equilateral triangle formed by extending the lines. This equilateral triangle therefore has an area of 7. This is also one sixth of the area of the original hexagon. The ultimate answer is therefore 42.