Question : In trapezium $ABCD$, $AB \parallel CD$ and $AB = 2CD$. Its diagonals intersect at $O$. If the area of $\triangle AOB=84\;\mathrm{cm^2}$ then the area of $\triangle COD$ is equal to:

Option 1: 72 cm²

Option 2: 21 cm²

Option 3: 42 cm²

Option 4: 26 cm²

Question : ABCD is a cyclic quadrilateral. Sides AB and DC, when produced, meet at E and sides AD and BC, meet at F. If $\angle $ADC = 76$^\circ$ and $\angle$AED = 55$^\circ$, then $\angle$AFB is equal to:

Option 1: $34^\circ$

Option 2: $26^\circ$

Option 3: $29^\circ$

Option 4: $27^\circ$

Question : ABCD is a quadrilateral. The length of the diagonal AC is 24 cm. The sum of the perpendicular drawn from vertex B and D on the diagonal AC is 10 cm. What is the area of the quadrilateral?

Option 1: 240 cm²

Option 2: 180 cm²

Option 3: 120 cm²

Option 4: 90 cm²

Question : ABCD is a quadrilateral in which BD and AC are diagonals. Then, which of the following is true:

Option 1: AB + BC + CD + DA < (AC + BD)

Option 2: AB + BC + CD + DA > (AC + BD)

Option 3: AB + BC + CD + DA = (AC + BD)

Option 4: AB + BC + CD + DA > 2(AC + BD)

Question : ABCD is a quadrilateral in which AB || DC. E and F are the midpoints of the diagonals AC and BD, respectively. If AB = 18 cm and CD = 6 cm, then EF =?

Option 1: 8 cm

Option 2: 6 cm

Option 3: 12 cm

Option 4: 9 cm