1. The area of a field in the shape of a trapezium is 1800 m². The perpendicular distance between its parallel sides is 30 m. If the ratio of the parallel sides is 7 : 5, then the length of the longer parallel side is:
a) 56 m
b) 63 m
c) 70 m
d) 84 m

2. The ratio of the lengths of the parallel sides of a trapezium is 5 : 3. The shortest distance between them is 12 cm. If the area of the trapezium is 384 cm², then the sum of the lengths of the parallel sides is:
a) 48 cm
b) 56 cm
c) 64 cm
d) 72 cm

3. The parallel sides of a trapezium are in the ratio 4 : 5 and the shortest distance between them is 14 cm. If the area of the trapezium is 567 cm², then the length of the longer parallel side is:
a) 35 cm
b) 40 cm
c) 45 cm
d) 49 cm

4. ABCD is a trapezium in which AB ∥ DC and AB = 3 DC. The diagonals AC and BD intersect at O. The ratio of the areas of triangles AOB and COD is:
a) 1 : 9
b) 3 : 1
c) 9 : 1
d) 1 : 3

5. The ratio of the lengths of the parallel sides of a trapezium is 5 : 3. The shortest distance between them is 12 cm. If the area of the trapezium is 384 cm², then the sum of the lengths of the parallel sides is:
a) 48 cm
b) 56 cm
c) 64 cm
d) 72 cm

6. ABCD is a trapezium with AD ∥ BC. Point E lies on BC such that BE : EC = 1 : 1. If AD = 10 cm and BC = 20 cm, then the ratio of the area of trapezium ABCD to that of triangle AED is:
a) 2 : 1
b) 3 : 1
c) 4 : 1
d) 5 : 1

7. The lengths of the two parallel sides of a trapezium are 10 cm and 14 cm. If the height of the trapezium is 5 cm, then its area is:
a) 50 cm²
b) 55 cm²
c) 60 cm²
d) 65 cm²

8. The lengths of the two parallel sides of a trapezium are 26 cm and 50 cm. If the length of each of the other two sides is 13 cm, then the area (in cm²) of the trapezium is:
a) 312
b) 336
c) 364
d) 390

9. The area of an isosceles trapezium is 150 cm² and the height is 1/5 of the sum of its parallel sides. If the ratio of the lengths of the parallel sides is 2 : 3, then the length of a diagonal (in cm) is:
a) 10
b) 12
c) 13
d) 15

10. In trapezium PQRS, PQ ∥ RS and PQ = 3 RS. The diagonals of the trapezium intersect at O. If the area of ∆POQ is 108 cm², then the area of ∆ROS is:
a) 12 cm²
b) 18 cm²
c) 24 cm²
d) 36 cm²

11. The lengths of the two parallel sides of a trapezium are 18 cm and 32 cm. If the area of the trapezium is 250 cm², then its height is:
a) 8 cm
b) 9 cm
c) 10 cm
d) 12 cm

12. In a trapezium PQRS, PQ ∥ RS, PQ < RS. If RS = 10 cm and the distance between the parallel sides is 5 cm. If the area of trapezium PQRS is 30 cm², then the length of PQ is:
a) 1 cm
b) 2 cm
c) 3 cm
d) 4 cm

13. In a trapezium PQRS, PQ ∥ RS and ∠PRS = 90°. If PQ = 14 cm, RS = 30 cm and diagonal PR = 34 cm, then the area of trapezium PQRS is:
a) 176 cm²
b) 192 cm²
c) 198 cm²
d) 210 cm²

14. In a trapezium PQRS, PQ ∥ RS. The diagonals intersect at point O. If PQ = 3 RS, then the ratio of the areas of ∆POQ and ∆ROS is:
a) 3 : 1
b) 5 : 1
c) 9 : 1
d) 27 : 1

15. The lengths of the two parallel sides of a trapezium are 18 m and 26 m respectively. If its height is 8 m, then the area of the trapezium (in square metres) is:
a) 160
b) 176
c) 192
d) 208

Answers