Provement

Join AQ and CP.

A(APC)= A(ABC)/2 …… (Since CP is a median)

In triangle APC,

Since CR is a median,

A(ARC)= 1/4 A(ABC)-------(1)

A(PRQ)= 1/2 A(APQ)= 1/2 A(BPQ)

A(BPQ)= 1/4 A(ABC)

or A(PRQ)= 1/8 A(ABC)

So. A(PRQ)= 1/2 A(ARC) [Since A(ARC)= 1/4 A(ABC)]

 

2). A(RQC)=A(RQB)

A(ABC)= A(RQB)+ A(RQC)+ A(ARC)

or A(ABC)= 2 A(RQC) + 1/4 A(ABC) [Using (1)]

or 2 A(RQC)= 3/4 A(ABC)

or A (RQC) = 3/8 A(ABC)