The area of a shape is the total number of square units that fill the shape.

When we divide a rectangle into squares with side length one, we see that
the width is the number of square units in a row and the height is the total
number of rows. Thus, the total number of squares inside the rectangle is equal
to the number of rows times the number of units in each row, or the height times
the width of the rectangle. Area of a Rectangle
= (*h*×*w*)
, where
*h*
is the height and
*w*
is the width. In the sample rectangle from
the previous section,
*h* = 3
and
*w* = 6
, so the area is
3×6 = 18
.
In other words, there are 18 squares in the interior of the rectangle:

Area of a Rectangle

When we divide a square into squares with side length one, we see that the
number of square units in a row is the same number of total rows, or that
*h* = *w*
.
Thus, the area of a square is equal to the length of a side times the length of
a side, or to the length of a side squared (the term
squared is no coincidence). Area of a
Square
= *s*
^{2}
, where
*s*
is the length of a side. In the
sample square from the previous section,
*s* = 8
, so the area is
8^{2} = 64
.
In a square of side length 3, the area is
3^{2} = 9
:

Areas of Two Squares