$PQRS$ is a rectangle. If $PQ = 20 \, cm$ and $\operatorname{ar}(PQRS) = 300 \, cm^2$,then $SP = \dots \, cm$.

In the figure,$CD \parallel AE$ and $CY \parallel BA$. Prove that $\operatorname{ar}(\triangle CBX) = \operatorname{ar}(\triangle AXY)$.

$ABCD$ is a quadrilateral whose diagonal $AC$ divides it into two parts of equal area. Then $ABCD$:

Observe the given figure. Does the parallelogram $ABCD$ and the triangle $QBC$ lie on the same base and between the same parallels? If yes,write the common base and the two parallels.

In the figure,$BD \parallel CA$,$E$ is the mid-point of $CA$,and $BD = \frac{1}{2} CA$. Prove that $\operatorname{ar}(ABC) = 2 \operatorname{ar}(DBC)$.

State whether each of the following statements is true or false:
$(1)$ If $ar(ABC) = 96 \, cm^2$ for the parallelogram $ABCD$,then $ar(ABCD) = 192 \, cm^2$.
$(2)$ Area of a right triangle = Product of the sides forming the right angle.