Question 1: In a parallelogram, if one side measures 8 cm and the height is 5 cm, calculate the area.

Answer: 40

Question 2: Construct a parallelogram with sides of 6 cm and 10 cm, where the angle between the sides is 60°. Use the grid to draw it accurately.

Answer:

Question 3: If the diagonals of a parallelogram are 10 cm and 14 cm, and they bisect each other, find the length of the sides assuming the parallelogram is a rhombus.

Answer: 7.5

Question 4: Fluency & Practice: The base of a parallelogram is 9 cm, and its height is 4 cm. What is the area?

Answer: 36

Question 5: Calculate the length of the hypotenuse in a right-angled triangle formed within a parallelogram where the sides are 7 cm and 24 cm.

Answer: 25

Question 6: A parallelogram has sides of 12 cm and 16 cm, and one of its angles is 70°. Use the law of cosines to find the length of the diagonal opposite this angle.

Answer: 20.5

Question 7: Real-world Application: A farmer wants to enclose a piece of land in the shape of a parallelogram. If one side is 150 meters long and the height is 80 meters, what is the total fencing needed?

Answer: 460

Question 8: Construct a parallelogram where the sides are 5 cm and 8 cm, and the angles are 60° and 120°. Use the grid to accurately draw it.

Answer:

Question 9: Challenge & Extension: Prove that the opposite angles in a parallelogram are equal using geometric properties. Fill in the missing steps on the diagram.

Answer:

Question 10: Error Analysis: A student claims the area of a parallelogram with base 10 cm and height 6 cm is 60 cm². Identify and correct the mistake if any.

Answer: The calculation is correct; area = base × height = 10 × 6 = 60 cm².