What is Area?

Area is the size of a surface!

Example:

These shapes all have the same area of 9:

Three different shapes each composed of 9 unit squares

Paint roller filling a square shape with color

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

Area of Simple Shapes

There are special formulas for certain shapes:

Example: What's the area of this rectangle?

Rectangle divided into a grid of 3 rows and 5 columns

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

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

Diagram comparing three 1-meter squares to one large 3 by 3 meter square

There are also "square mm", "square cm" and so on, 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:

more than half a square counts as 1
less than half a square counts as 0

Like this:

Irregular pentagon on a grid with dots indicating squares to 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

Where:

π = the number pi (3.1416...)
r = radius

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's the area of this Shape?

area grass

Let's break the area into two parts:

L-shaped area split into a square labeled A and a triangle labeled 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 = 12 × b × h = 12 × 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 = 12× b × h) and add them all up.

Area by Coordinates

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

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

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

Garden Area Activity