Question

In △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.

Answer 1

Answer:

Step-by-step explanation:

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

Answer: 7 sq. cm