IIMB 2002 (QA) PYQs

The perimeter of a rhombus is $148 \text{ cm}$ and one of its diagonals is $70 \text{ cm}$. Its area is equal to the area of a trapezium whose parallel sides are $x \text{ cm}$ and $50 \text{ cm}$ and the distance between the parallel sides is $14 \text{ cm}$. What is the value of $x$?

In the given diagram, $ABCD$ is a trapezium. If $AB=4$ cm, $CD=6$ cm and $OB=5$ cm, then what is the length of $OD.$

$ABCD$ is a quadrilateral. The diagonals of $ABCD$ intersect at the point $P$. The area of the triangles $APD$ and $BPC$ are $27$ and $12$, respectively. If the areas of the triangles $APB$ and $CPD$ are equal then the area of triangle $APB$ is