Find Sides, Height, Angles, and Diagonals of Parallelogram

1. A parallelogram has sides 12 cm and 8 cm. Find its perimeter.
   
2. In a parallelogram, the base is 15 cm and the height is 10 cm. Find its area.
   
3. A parallelogram has sides 10 cm and 6 cm. If the height corresponding to the 10 cm side is 4 cm, find the area.
   
4. The opposite angles of a parallelogram are in the ratio 3:2. Find all angles of the parallelogram.
   
5. The diagonals of a parallelogram are 10 cm and 6 cm. If they bisect each other at right angles, find its area.
   
6. A parallelogram has an area of 60 cm² and base 12 cm. Find the height.
   
7. In a parallelogram ABCD, AB = 10 cm and BC = 8 cm. Find the perimeter.
   
8. The diagonals of a parallelogram intersect at point O. If one diagonal is 12 cm and the other is 16 cm, find the lengths of segments AO, BO, CO, and DO.
   
9. A parallelogram has angles 70° and 110°. Find the remaining angles.
   
10. The base of a parallelogram is 14 cm and the corresponding height is 9 cm. Find the area.
    
11. Find the perimeter of a parallelogram whose sides are in the ratio 3:5 and the sum of the sides is 32 cm.
    
12. In a parallelogram, one angle is 65°. Find all other angles.
    
13. The height of a parallelogram is half of its base. If the base is 10 cm, find its area when the height is used.
    
14. A parallelogram has sides 8 cm and 6 cm, and the height corresponding to 8 cm side is 5 cm. Find the area.
    
15. Find the length of a side of a parallelogram whose area is 48 cm² and the height is 6 cm.
    
16. A parallelogram has diagonals intersecting at right angles. One diagonal is 12 cm and the other is 16 cm. Find its area.
    
17. In a parallelogram, adjacent angles are in the ratio 2:3. Find all angles.
    
18. A parallelogram has sides 7 cm and 10 cm. If the height corresponding to the 10 cm side is 6 cm, find its area.
    
19. The diagonals of a parallelogram are equal. What type of parallelogram is it?
    
20. In a parallelogram, one diagonal divides it into two congruent triangles. Prove that the area of each triangle is half of the parallelogram.
    
21. A parallelogram has sides 12 cm and 8 cm. Find its perimeter.
22. In a parallelogram, the base is 15 cm and the height is 10 cm. Find its area.

23. A parallelogram has sides 10 cm and 6 cm. If the height corresponding to the 10 cm side is 4 cm, find the area.

24. The opposite angles of a parallelogram are in the ratio 3:2. Find all angles of the parallelogram.

25. The diagonals of a parallelogram are 10 cm and 6 cm. If they bisect each other at right angles, find its area.

26. A parallelogram has an area of 60 cm² and base 12 cm. Find the height.

27. In a parallelogram ABCD, AB = 10 cm and BC = 8 cm. Find the perimeter.

28. The diagonals of a parallelogram intersect at point O. If one diagonal is 12 cm and the other is 16 cm, find the lengths of segments AO, BO, CO, and DO.

29. A parallelogram has angles 70° and 110°. Find the remaining angles.

30. The base of a parallelogram is 14 cm and the corresponding height is 9 cm. Find the area.

31. Find the perimeter of a parallelogram whose sides are in the ratio 3:5 and the sum of the sides is 32 cm.

32. In a parallelogram, one angle is 65°. Find all other angles.

33. The height of a parallelogram is half of its base. If the base is 10 cm, find its area when the height is used.

34. A parallelogram has sides 8 cm and 6 cm, and the height corresponding to 8 cm side is 5 cm. Find the area.

35. Find the length of a side of a parallelogram whose area is 48 cm² and the height is 6 cm.

36. A parallelogram has diagonals intersecting at right angles. One diagonal is 12 cm and the other is 16 cm. Find its area.

37. In a parallelogram, adjacent angles are in the ratio 2:3. Find all angles.
38. A parallelogram has sides 7 cm and 10 cm. If the height corresponding to the 10 cm side is 6 cm, find its area.

39. The diagonals of a parallelogram are equal. What type of parallelogram is it?

40. In a parallelogram, one diagonal divides it into two congruent triangles. Find the area of each triangle.

41. The base of a parallelogram is 18 cm and the height is 12 cm. Find its area.

42. A parallelogram has sides 9 cm and 6 cm. Find its perimeter.

43. In a parallelogram, one angle is 120°. Find all remaining angles.

44. A parallelogram has base 15 cm, height 8 cm. Find its area.

45. The sides of a parallelogram are 14 cm and 10 cm. Find the perimeter.

46. A parallelogram has sides in ratio 5:3, perimeter 64 cm. Find each side.

47. In a parallelogram, one angle is 75°. Find all angles.

48. The diagonals of a parallelogram are 12 cm and 16 cm. Find its area if they intersect at right angles.

49. A parallelogram has base 20 cm, height 5 cm. Find its area.

50. A parallelogram has sides 11 cm and 7 cm. Find its perimeter.

51. In parallelogram ABCD, AB = 12 cm, BC = 8 cm, and the height corresponding to AB is 7 cm. Find the area and perimeter.
    
52. A parallelogram has angles ∠A = 70° and ∠B = 110°. Find all other angles.
    
53. The diagonals of parallelogram PQRS intersect at right angles. If one diagonal is 10 cm and the other is 6 cm, find the area.
    
54. In parallelogram EFGH, the sides are in ratio 3:5, and the perimeter is 64 cm. Find each side.
    
55. The base of a parallelogram is 14 cm, and its area is 98 cm². Find the corresponding height.
    
56. Parallelogram KLMN has adjacent angles in the ratio 2:3. Find all angles.
    
57. In parallelogram ABCD, diagonals AC = 16 cm and BD = 12 cm intersect at O. Find the lengths AO, BO, CO, and DO.
    
58. A parallelogram has sides 10 cm and 6 cm. The height corresponding to the longer side is 5 cm. Find the area and perimeter.
    
59. Parallelogram XYZW has angles in ratio 3:2. If the longer side is 15 cm, find all angles and the perimeter.
    
60. In a parallelogram, one angle is 65°, and the adjacent side is 12 cm. Find all angles and the perimeter.
    
61. The diagonals of a parallelogram are equal, and its sides are 10 cm and 6 cm. Identify the type of parallelogram and find its perimeter.
    
62. A parallelogram has base 20 cm, side 15 cm, and height corresponding to the base 12 cm. Find area, perimeter, and angles if one angle is 120°.
    
63. Parallelogram ABCD has sides AB = 8 cm, BC = 5 cm. If the diagonals intersect at 90°, find its area.
    
64. In parallelogram PQR S, angles are 3x and 2x. If one side is 10 cm and height 6 cm, find the area and all angles.
    
65. A parallelogram has sides 9 cm and 12 cm. The height corresponding to the longer side is 8 cm. Find area and perimeter.
    
66. The perimeter of a parallelogram is 64 cm. One side is longer than the other by 4 cm. Find the lengths of the sides.
    
67. In a parallelogram, one angle is twice the other. Find all four angles.
    
68. A parallelogram has base 18 cm, height 12 cm, and side 15 cm. Find area, perimeter, and angles if one angle is 120°.
    
69. Diagonals of a parallelogram intersect at right angles. If they are 14 cm and 10 cm, find the area.
    

70.A parallelogram has sides 11 cm and 7 cm. The height corresponding to the longer side is 6 cm. Find area, perimeter, and angles.