What is Area?

Area is the size of a surface!


These shapes all have the same area of 9:

same area of 9

area paint


It helps to imagine how much paint would cover the shape.

Area of Simple Shapes

There are special formulas for certain shapes:

Example: What is the area of this rectangle?

Area Count

The formula is:

Area = w × h
w = width
h = height

The width is 5, and the height is 3, so we know w = 5 and h = 3:

Area = 5 × 3 = 15

Learn more at Area of Plane Shapes.

Area by Counting Squares

We can also put the shape on a grid and count the number of squares:

Area Count
The rectangle has an area of 15

Example: When each square is 1 meter on a side, then the area is 15 m2 (15 square meters)

Square Meter vs Meter Square

The basic unit of area in the metric system is the square meter, which is a square that has 1 meter on each side:

1 Square Meter
1 square meter

Be careful to say "square meters" not "meters squared":

3 Square Meters vs 3 meters squared

There are also "square mm", "square cm" etc, learn more at Metric Area.

square cm

Approximate Area by Counting Squares

Sometimes the squares don't match the shape exactly, but we can get an "approximate" answer.

One way is:

Like this:

Area Count
This pentagon has an area of approximately 17


Or we can count one square when the areas seem to add up.

Example: Here the area marked "4" seems equal to about 1 whole square (also for "8"):

Area Count
This circle has an area of approximately 14


But using a formula (when possible) is best:

Example: The circle has a radius of 2.1 meters:

area circle 2.1 radius

The formula is:

Area = π × r2


The radius is 2.1m, so:

Area = 3.1416... × (2.1m)2
= 3.1416... × (2.1m × 2.1m)
= 13.854... m2

So the circle has an area of 13.85 square meters (to 2 decimal places)

Area of Difficult Shapes

We can sometimes break a shape up into two or more simpler shapes:

Example: What is the area of this Shape?

area grass

Let's break the area into two parts:

area grass zone A and B

Part A is a square:

Area of A = a2 = 20m × 20m = 400m2

Part B is a triangle. Viewed sideways it has a base of 20m and a height of 14m.

Area of B = ½b × h = ½ × 20m × 14m = 140m2

So the total area is:

Area = Area of A + Area of B

Area = 400m2 + 140m2

Area = 540m2

Area by Adding Up Triangles

We can also break up a shape into triangles:

area 3 triangles

Then measure the base (b) and height (h) of each triangle:

area 3 triangles with base and height

Then calculate each area (using Area = ½b × h) and add them all up.


area irregular polygon

Area by Coordinates

When we know the coordinates of each corner point we can use the Area of Irregular Polygons method.

There is an Area of a Polygon by Drawing Tool that can help too.


774, 3245, 775, 776, 2161, 2162, 3246, 3247, 3248, 3249