Relation between Area and Sides of Similar Triangles

Q.

In given figure $△$ ABC and $△$ DEF are similar, EF=3cm, BC=4cm, and area of triangle DEF=54$c{m}^2$ . Find the area of $△$ ABC.

___ $c{m}^2$.

Q. BD is a median of a triangle ABC. F is a point on AB such that CF intersects BD at E and $BE=BD$. If $BF=5$ cm. BA is equal to

1. 10
2. 12
3. 15
4. 17

Q. ABCD is a parallelogram. P is a point on AD such that $AP=\frac{1}{3}AD$ and Q is a point on BC such that $CQ=\frac{1}{3}BC$. Prove that AQCP is a parallelogram.

Q. In the given figure, $AP=DP$, $\angle A=\angle D$ and $\angle B=\angle C={90}^o$
which of the following is correct

1. $P$ is the mid-point of $BC$
2. $△ABP\cong △DCP$
3. $AB=DC$
4. $AB=PB$