Question 1: Calculate the area of a square with a side length of 7 cm.

Answer: 49

Question 2: A square has a perimeter of 48 meters. Find the length of one side.

Answer: 12

Question 3: Construct a square where each side measures 5 cm. Calculate its diagonal using Pythagoras' theorem.

Answer: 7.07

Question 4: Explain why all sides of a square are equal and how this property can be used to differentiate a square from other quadrilaterals.

Answer: In a square, all four sides are equal in length, which helps distinguish it from rectangles or rhombuses where only opposite sides are equal. This property is key in identifying and constructing squares.

Question 5: A farm has a square plot of land with an area of 625 square meters. Find the length of each side.

Answer: 25

Question 6: A square tile measures 30 cm on each side. If you cut four identical smaller squares from the corners and fold the remaining shape into a box, what is the volume of the box if the cut-out squares are 5 cm each?

Answer: 250

Question 7: Calculate the length of the diagonal of a square with a side of 9 cm.

Answer: 12.73

Question 8: A square's side length is doubled. How does this affect its area? Provide a mathematical explanation.

Answer: The area increases by a factor of four because area is proportional to the square of the side length. If side length doubles, area becomes four times larger.

Question 9: Given a square with an area of 81 cm², find its perimeter.

Answer: 36

Question 10: Identify and correct the mistake in the following statement: 'All sides of a square are equal, but the diagonals are not necessarily equal to the sides.'

Answer: The statement is incorrect because in a square, the diagonals are equal in length and are √2 times the length of a side. Therefore, diagonals are always longer than the sides.

Question 11: A square garden measures 20 meters on each side. If a pathway of width 2 meters is built inside along the perimeter, what is the area of the pathway?

Answer: 72

Question 12: Challenge: Prove that the sum of the squares of the diagonals of a square is equal to twice the square of its side.

Answer: 2s²