Find the ratios of the four areas.

Consider  the 3 x 3  square below

The whole area  = 3 * 3    =  9

The area  of  triangle MPC  =  (1/2) (1.5) (1)   =  .75

The area of triangle BPC =  (1/2) (3)(1)  =  3/2  = 1.5

Area of triangle APB  =  (1/2) (3) (2)    = 3

So the area of the  remaining quadrilateral  = is  9  - .75 - 1.5  - 3   = 3.75

The only question I have is  the ratios  of  what  ???.....of each area to the whole area  ???

If so

MPC / 9  =     .75/9   =  1/12

BPC / 9    =   1.5/9  =    2/12 =  1/6

APB / 9   =  3/9 =   4/12 =   1/4

And  APMD  / 9   =  3.75/9  =  5/12

PC : AP = 1 : 2        MP : BP = 1 : 2

[MPC] = 1/12 [ABCD]           [BPC] = 1/6 [ABCD]

[APB] = 1/3 [ABCD]              [APMD] = 5/12 [ABCD]

[MPC] : [BPC] : [APB] : [APMD] = 1 : 2 : 4 : 5