Question

P, Q and R are the mid points of the sides of $\Delta$ABC and X, Y and Z are the mid points of $\Delta$PQR. If area of $\Delta$XYZ is $10$ then find the area of $\Delta$ PQR.

Answer 1

Given:

$Ar\left(△XYZ\right)=10$

as $X,Y$ and $Z$ are midpoint of $PQ,QR$ and $PR$

we know that

$Ar\left(△XYZ\right)=\frac{1}{4}Ar\left(PQR\right)$

$\therefore Ar\left(△PQR\right)=4\left(10\right)=40$

$Ar\left(△PQR\right)=40$