If you scale the entire figure by x in the horizontal direction and 1/x in the vertical dimension all of the areas will be preserved. By setting x to the fourth root of 3 (approximately 1.316) the equilateral triangles are all transformed into right-angled isosceles triangles with height half of their bases, so that a triangle with area n^2 will have height n and base 2n. Now it is simple to find the area of the trapezoid of base 19, and then subtract the triangles and half triangles to find the required area.

The trapezoid has area 19x7/2, from which we must subtract 16/2, 9, 1, 4 and 9/2.

The answer is therefore 40 square units.