Question 1: A gaming console controller has a parallelogram-shaped touchpad with a base of 10 cm and a height of 4 cm. Calculate the area of the touchpad.

Answer: 40

Question 2: Construct a parallelogram on the grid with a base of 6 cm and a side length of 5 cm, where the sides are parallel and equal in length.

Answer: Constructed shape with correct sides and angles

Question 3: In a VR headset, a parallelogram-shaped display panel has a length of 15 cm and a width of 8 cm. If the panel is tilted, forming a parallelogram with a slant height of 10 cm, what is the area of the panel?

Answer: 120

Question 4: A parallelogram-shaped gaming frame has sides measuring 12 cm and 9 cm, with the angles between sides being 60°. Determine the area of the frame.

Answer: 93.53

Question 5: A designer creates a parallelogram-shaped digital display with a base of 20 cm and a height of 7 cm. The display is rotated, forming a slanted parallelogram with a side length of 15 cm. Calculate the area of the display.

Answer: 140

Question 6: Explain how the property that diagonals of a parallelogram bisect each other can be used to verify the shape of a digital screen segment in gaming.

Answer: By checking if the diagonals bisect each other, one can confirm the segment is a parallelogram, ensuring accurate display alignment in gaming interfaces.

Question 7: A parallelogram-shaped screen has a base of 18 cm and a height of 9 cm. If the width of the screen is increased by 4 cm, maintaining the same height, what is the new area?

Answer: 252

Question 8: A gaming chair has a parallelogram-shaped side panel with a length of 14 cm and a perpendicular height of 6 cm. If the side panel’s area is 84 cm², what is the length of the base?

Answer: 12

Question 9: Design a parallelogram-shaped component for a virtual reality headset, with a side length of 8 cm and a base of 10 cm. If the component is slanted so that the height is 6 cm, what is its area?

Answer: 48

Question 10: Identify and correct the mistake in the following statement: 'The diagonals of a parallelogram are equal in length.'

Answer: Diagonal lengths are not necessarily equal; in a general parallelogram, diagonals bisect but may differ in length.