Let M and N be the midpoints of AB and CD.
The ratio in which each diagonal is divided is equal to the ratio of the lengths of the parallel sides.
AB/CD = AP/PC = BP/PD = 2/3 The ratio of MP to NP is 2/3 also
If CD = 8 then AB = 8 * (2/3) = 5.33333333333
NP = 9 / 4 = 2.25
MP = 2.25 * (2/3) = 1.5
The height of the trapezium is h = MP + NP = 3.75
Area of the trapezium is A = h/2 ( AB + CD ) = 25 cm2
The area of the triangle BCP Abcp = ( 25 - 13 ) / 2