Final answer:
To construct a square with side length ab, draw four equal straight lines ab long at right angles. The perimeter will be 4ab and the area ab². A larger square with each side twice the length will have four times the area.
Step-by-step explanation:
To construct a square with sides of length ab, you would follow this process:
Start by drawing a straight line that is the length of ab.
Use a right angle tool to draw a perpendicular line from one end of the first line, making sure it is also the length of ab.
From the other end of the initial line, draw another perpendicular line that is ab in length, ensuring that it is parallel to the second line you drew.
Connect the ends of the second and third lines to create the fourth side of the square.
Understanding that the perimeter is simply 4 times the side length (4ab) and the area is the side length squared (ab²), is crucial in constructing squares. If the length is 3 meters, then the perimeter would be 12 meters, and the area would be 9 square meters.
If another square has dimensions that are twice the first, then the side length of the larger square is 2ab. Therefore, its area is four times the area of the smaller square, since (2ab²) is equal to 4ab².
This extends to three-dimensional objects like cubes, where the volume is the cube of the side length (ab³).