The area of a closed two-dimensional object measures the space enclosed by the perimeter of the shape.  An example of when area would be used is if we wished to carpet a room.  We would need to know the amount of carpet needed, and the area of the room (either in yards, feet, or meters) would be required.

Area is measured in square units, meaning that area tells us the number of these squares we would need to contain the space.  If we have a rectangular shape and we wanted to know the area in feet, we would find the number of squares, each side measuring 1 foot, that fit inside the rectangular shape.

The example below shows a square that measures 10 feet by 10 feet.  I can draw 100 1x1ft boxes inside this square.  Therefore the area of this square is 100 square feet, written 100 ft².

We can use formulas that have already been calculated to help us find the areas of different kinds of objects, including circles.  In the above example, we can see that the area of a square is found by multiplying the length of its sides.  The area of a rectangle is found by multiplying the length by its width.  The units must be the same for these formulas to work properly.

This formula sheet provides area formulas for several different kinds of shapes.  Look for the formulas that start with "A = ..."

If you have a composite shape, that is, a shape that is irregular, you can find its area by dividing it up into shapes that you know, finding the area of each of these shapes, and then adding the areas together.

These class notes provide further explanation and examples of area and circumference.