P, Q, R are the mid-points of the sides of ΔABC. X, Y, Z are the mid-points of the sides of ΔPQR. If the area of ΔXYZ is 10, find the area of APQR and the area of ΔABC.

In ∆ABC, P, Q, R are the mid-points of the sides AB, BC and CA respectively.

The correspondence ∆ABC↔∆QRP is a similarity.

Areas of similar triangles are proportional to the squares of their corresponding sides.

∆ABC = ∆POR

Similarly, X,Y and Z are the mid-points of the sides of ∆PQR, we get

∆PQR = 4∆XYZ

∆PQR = 4×10

∆PQR = 40

Thus, the area of ∆PQR is 40 sq. units.

∆ABC = 4∆PQR

∆ABC = 4×40

∆ABC = 160

Hence, the area of ∆ABC is 160 sq. units.