# A Square Investigation: Length, Perimeter and Area

- Author:
- chudson

Objective: Determine the effect on the perimeter and the area of square when the length of a side is changed.
Procedure:
1.) Drag points B and C to change the dimensions of the square. Make a table of values showing the length of a side, the perimeter and the area of different size squares.
2.) Use the results to answer the questions listed below.
3.) Change the original figure to a rectangle. Drag points B and C to change the dimensions. Make a table of values showing the length and width of the rectangle, the perimeter and the area of

**similar**rectangles.Questions:
1.) If the length of the side of a square is doubled, what is the effect on the perimeter and area of the square?
2.) If the length of the side of a square is tripled, what is the effect on the perimeter and area of the square?
3.) If the length of the side of a square is multiplied by a factor of 4 (quadrupled), what is the effect on the perimeter and area of the square?
4.) If the length of the side of a square is halved, what is the effect on the perimeter and area of the square?
5.) If the length of the side of a square is multiplied by a factor X, what is the effect on the perimeter and area of the square?
6.) Write a conjecture explaining how the perimeter and area of a square are affected by a change in the length of the side of the square.
7.) Can you show algebraically that your conjecture is true?
8.) Would your conjecture hold true, if the figure being investigated was some other polygon (rectangle, triangle, pentagon, etc.)?