Definition: In geometry, a square is a 2-dimensional figure with four equal sides and four right (90°) angles.

Interactivity 1: Square    Directions for interactivity

Click and drag points A and B to resize, move and rotate.

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Basic formulas for square with side a : perimeter is: L=4a , and area is: A=a^2 .

Examples with perimeter and area of square

Side length: a Perimeter: L=4a Area: A=a^2
3 \,cm 4 \cdot 3\,cm=12\,cm 3 \,cm \cdot 3 \,cm=3^2 \,cm^2=9 \,cm^2
2,5 \,m 4 \cdot 2,5 \,m=10 \,m 2,5 \,m \cdot 2,5 \,m=(2,5)^2 \,m^2=6,25 \,m^2
Interactivity 2: Construct a square.
1. Check out the square in the left window.
 1.a Choose the icon.
 1.b Click and drag the slider button to increase or decrease the square size as desired.
 1.c Click and drag the point B to slant the square as desired.
Notice that the square ALWAYS remains a square.
2. You do it in the right window.
 2.a Construct a square in the right window with the same properties.
 2.b If you need help, click to open a new window with complete directions.
Check that the square ALWAYS remains a square.
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Equivalent Definitions:

Theorems

  • The diagonals of a square are of equal length (follows because a square is a rectangle).
  • The diagonals of a square intersect at right 90° angle (follows because a square is a rhombus).

Related themes:


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Page last modified on January 28, 2009, at 08:24 AM