1. Construction of FH to form 2 pairs of similar triangles (double deck ABC & FBH, hour-glass BCG & HFG) 2. Double deck similar triangles with side ratio 1:2 Hence FH:AE= 1.5:3 3. To have integers for all horizontal side ratios BC:FH:AE = 10:3:6 4. Trapezium BCHF has top:bottom ratio 10:3. Hence 4 triangles of trapezium dissected by diagonals has area ratios 10^2:10x3:10x3:3^2 = 100(top):30(left):30(right):9(bottom) Top + left = 1/4 of whole parallelogram. Hence parallelogram has 4 x (100 + 30) = 520 parts Left + bottom = triangle BFH = 1/4 of triangle ABE. Hence ABE has 4x(30 + 9) = 156 parts. Quadrilateral AFHE = triangle ABE - triangle BFH has 156 - 39 = 117 parts Quadrilateral AFGE with given area = quadrilateral AFHE + triangle FGH (bottom) has 117 + 9 = 126 parts Quadrilateral AFGE gives actual area: ratio area = 42:126 = 1:3 5. Quadrilateral CDEG = parallelogram ABCD - triangle FBC - quadrilateral AFGE Hence number of parts = 520 - 130 - 126 = 264 parts Actual area = 264 x (1/3) = 88
