Answer :

(i) We know that each median of a triangle divides it into two triangles of equal area.

Since,


CR is a median of ΔCAP


Therefore,


Area (ΔCRA) = Area (ΔCAP) (i)


Also,


CP is a median of ΔCAB


Therefore,


Area (ΔCAP) = Area (ΔCPB) (ii)


From (i) and (ii), we get


Therefore,


Area (ΔARC) = Area (ΔCPB) (iii)


PQ is a median of ΔPBC


Therefore,


Area (ΔCPB) = 2 Area (ΔPQB) (iv)


From (iii) and (iv), we get


Area (ΔARC) = Area (ΔPBQ) (v)


(ii) Since QP and QR medians of ΔQAB and QAP respectively.


Area (ΔQAP) = Area (ΔQBP) (vi)


And,


Area (ΔQAP) = 2 Area (ΔQRP) (vii)


From (vi) and (vii), we get


Area (ΔPRQ) = Area (ΔPBQ) (viii)


From (v) and (viii), we get


Area (ΔPRQ) = Area (ΔARC) (ix)


(iii) Since CR is a median of ΔCAP


Therefore,


Area (ΔARC) = Area (ΔCAP)


= * Area (ΔABC) (Therefore, CP is a median of Δ ABC)


= Area (ΔABC) (x)


Since,


RQ is a median of Δ RBC.


Therefore,


Area (ΔRQC) = Area (ΔRBC)


=[Area (ΔABC) – Area (ΔARC)]


= [Area (ΔABC) - Area ()]


= Area (Δ ABC)


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