Question : ABCD is a trapezium with AD and BC parallel sides and E is a point on BC. The ratio of the area of ABCD to that of AED is:

Option 1: $\mathrm{\frac{AD}{BC}}$

Option 2: $\mathrm{\frac{BE}{EC}}$

Option 3: $\mathrm{\frac{AD+BE}{AD+CE}}$

Option 4: $\mathrm{\frac{AD+BC}{AD }}$

Question : In a trapezium ABCD, AB and DC are parallel sides and $\angle ADC=90^\circ$. If AB = 15 cm, CD = 40 cm and diagonal AC = 41 cm, then the area of the trapezium ABCD is:

Option 1: 245 cm²

Option 2: 240 cm²

Option 3: 247.5 cm²

Option 4: 250 cm²

Question : The difference between the length of two parallel sides of a trapezium is 12 cm. The perpendicular distance between these two parallel sides is 60 cm. If the area of the trapezium is 1380 cm², then find the length of each of the parallel sides (in cm).

Option 1: 27, 15

Option 2: 31, 19

Option 3: 29, 17

Option 4: 24, 12

Question : ABCD is a trapezium where AD$\parallel$ BC. The diagonal AC and BD intersect each other at the point O. If AO = 3, CO = $x-3$, BO = $3x-19$, and DO = $x-5$, the value of $x$ is:

Option 1: -8, 9

Option 2: 8, -9

Option 3: -8, -9

Option 4: 8, 9

Question : Diagonals of a trapezium $ABCD$ with $AB \parallel CD$ intersect each other at the point $O$. If $AB = 2CD$, then the ratio of the areas of $\triangle AOB$ and $\triangle COD$ is:

Option 1: $4:1$

Option 2: $1:16$

Option 3: $1:4$

Option 4: $16:1$