N△abc points m and q are points on the sides ab and bc respectively, so that am=2mb and bq=qc. find area of quadrilateral mbqp if aq ∩ cm =p and aabc=30 cm2.

Denote the area of quadilateral MBQP as A, the area of the triangle MBP as and the area of the triangle BPQ as

Note that:

1.

2.

3.

4.

Now

You get the system of three equations:

Substitute the first equation into the last two:

From the first equation and then

Thus,

and

7 sq. cm