Question 1: Calculate the perimeter of a square piano frame that has each side measuring 2.5 meters.

Answer: 10 meters

Question 2: Find the area of a square soundproof panel with a side length of 1.8 meters.

Answer: 3.24 square meters

Question 3: A speaker enclosure is designed as a perfect square with an area of 16 square meters. What is the length of each side?

Answer: 4 meters

Question 4: Plot the graph of y=3x on the grid to represent how the length of a side increases with the number of sound channels.

Answer: Students will draw the line; no specific answer

Question 5: Construct a square with a perimeter of 20 units. Use the grid to sketch the square.

Answer: Side length = 5 units

Question 6: A music studio has a square room with a side length of 6 meters. If soundproofing material costs $15 per square meter, what is the total cost to cover all four walls?

Answer: $360

Question 7: A square-shaped acoustic panel measures 2.2 meters on each side. Calculate its perimeter and area.

Answer: {"area":"4.84 square meters","perimeter":"8.8 meters"}

Question 8: A square speaker grille has a side length of 0.75 meters. If a new grille is designed to double its area, what will be the new side length?

Answer: 1.5 meters

Question 9: A sound engineer mistakenly measured the side of a square panel as 3 meters instead of 3.5 meters. Identify and correct the error to find the actual area.

Answer: Incorrect measurement led to an underestimated area; correct side length = 3.5 m, area = 12.25 m²

Question 10: A square is inscribed in a circle such that all four corners touch the circle. If the circle's radius is 4 meters, find the side length of the square.

Answer: 4√2 meters

Question 11: A rectangular sound chamber has a square floor plan measuring 5 meters by 5 meters. If the length of the chamber is doubled, how does the volume change if the chamber's height remains 3 meters?

Answer: Volume doubles, from 75 m³ to 150 m³

Question 12: Challenge: Derive a formula for the diagonal length of a square in terms of its side length, and calculate the diagonal for a square with side 3 meters.

Answer: Diagonal = side × √2; for side 3 m, diagonal = 3√2 meters