Question : In a trapezium, one diagonal divides the other in the ratio $2:9$. If the length of the larger of the two parallel sides is 45 cm, then what is the length (in cm) of the other parallel side?

Option 1: $10$

Option 2: $5$

Option 3: $18$

Option 4: $14$

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 : The lengths of the two parallel sides of a trapezium are 28 cm and 40 cm. If the length of each of its other two sides is 12 cm, then the area (in cm²) of the trapezium is:

Option 1: $312\sqrt{5}$

Option 2: $408\sqrt{3}$

Option 3: $204\sqrt{3}$

Option 4: $504\sqrt{3}$

Question : The area of an isosceles trapezium is 176 cm² and the height is $\frac{2}{11}$th of the sum of its parallel sides. If the ratio of the length of the parallel sides is 4 : 7, then the length of a diagonal (in cm) is:

Option 1: $28$

Option 2: $\sqrt{137}$

Option 3: $2\sqrt{137}$

Option 4: $24$

Question : $ABCD$ is a parallelogram in which $AB = 7 \operatorname{cm}, BC = 9 \operatorname{cm}$, and diagonal $AC = 8 \operatorname{cm}$. What is the length (in cm) of the other diagonal?

Option 1: $14$

Option 2: $14\sqrt{2}$

Option 3: $7$

Option 4: $7\sqrt{2}$

Question : A metallic cube has sides of length 12 cm. It is melted and recast into three small cubes. Of these cubes, two have sides measuring 6 cm and 8 cm, respectively. The length of each side of the third cube is:

Option 1: 7 cm

Option 2: 9 cm

Option 3: 10 cm

Option 4: 5 cm