

Area of a Square
From Latin: area  "level ground, an open space,"
The number of square units it takes to completely fill a square.
Formula: Width × Height
Try this Drag the orange dots to move and resize the square. As the size of the square
changes, the area is recalculated.
Area formula
The area of a square is given by the formula area = width × height But since the width and height are by definition the same,
the formula is usually written as
area = s^{2}
where s is the length of one side.
In strictly correct mathematical wording the formula above should be spoken as "s raised to the power of 2", meaning s is multiplied by itself.
But we usually say it as "s squared". This wording actually comes from the
square. The length of a line s multiplied by itself, creates the square of side s. Hence "s squared".
Calculator
Use the calculator on the right to calculate the properties of a square.
Enter any one value and the other three will be calculated. For example, enter the side length and the area will be calculated.
Similarly, if you enter the area, the side length needed to get that area will be calculated.
The "diagonals" method
If you know the lengths of the diagonals, the area is half the product of the diagonals.
Since both diagonals are
congruent (same length), this simplifies to:

where
d is the length of either diagonal


Coordinate Geometry
If you know the
coordinates
of the
vertices
of a square, you can calculate all the other properties, including the area.
For more on this, see
Area and Perimeter of a square (Coordinate geometry)
Things to try
 In the figure above, click on "hide details"
 Drag the orange dots on the vertices to make a randomsize square.
 Now try to estimate the area of the square just looking at the small unit squares inside it
When you done click "show details" to see how close you got.
Other polygon topics
General
Types of polygon
Area of various polygon types
Perimeter of various polygon types
Angles associated with polygons
Named polygons
(C) 2009 Copyright Math Open Reference. All rights reserved

