What is Area?

Area is the size of a surface!

Example:

These shapes all have the same area of 9:

same area

 

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

If each square was 1 cm on a side, then the area would be 15 cm2 (15 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:

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:

The formula is:

Area = π × r2
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)
= 13.8544... 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?

Let's break the area into two parts:

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 = 400m2 + 140m2 = 540m2

Area by Adding Up Triangles

We can also break up a shape into triangles:

 

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

 

Then calculate each area (using Area = ½b × 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 is an Area of a Polygon by Drawing Tool that can help too.