The area of a
polygon
is the number of square units inside the polygon. To understand the difference between
perimeter
and area, think of perimeter as the length of fence needed to enclose the yard, whereas area is the space
inside the yard. Perimeter is 1dimensional and is measured in linear units such as inches, feet or meters.
Area is 2dimensional: it has a length and a width. Area is measured in square units such as square inches,
square feet or square meters.



To find the area of a
rectangle,
multiply the length by the width. The formula is:


,
where is the area,
is the length,
is the width,
and · means multiply.


A square is a rectangle with 4 equal sides.
To find the area of a square, multiply the length of one side by itself. The formula is:


or ,
where A is the area, s is the length of a side, and · means multiply.


Let's look at some examples of finding the area of rectangles.



Example 1:

Find the area of a square with each side measuring 2 inches.


Solution:



= (2 in) · (2 in) = 4 in^{2}


Example 2:

A rectangle has a length of 8 centimeters and a width of 3 centimeters. Find the area.


Solution:



= (8 cm) · (3 cm) = 24 cm^{2}



In Examples 1 and 2, we found the area given the dimensions
of the rectangle. Let's look at some examples in which we are given the area of the rectangle,
and are asked to work backwards to find the missing dimension. 


Example 3:

The area of a square is 9 square centimeters. How long is one side?


Solution:



9 cm^{2} = ·


Since 3 · 3 = 9, we get 3 cm · 3 cm = 9 cm^{2}.
So must equal 3 cm.


= 3 cm


Example 4:

The area of a rectangle is 12 square inches and the width is 3 inches. What is the length?


Solution:



12 in^{2} = · 3 in


Since 4 · 3 = 12, we get (4 in) · (3 in) = 12 in^{2}.
So must equal 4 in.


= 4 in



Summary: 
The dimensions of a rectangle are length and width.
Given the length and width of a rectangle, we can find the area. Given the area
and one dimension of a rectangle, we can find the other dimension. The formula
for area of a rectangle is:



where
is the length and
is the width.



A square is a rectangle with 4 equal sides The formula for area of a square is:



or
where
is the length of one side.
