What is Area?

Area is the size of a surface!

Example:

These shapes all have the same area of 9:

same area

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. So:

Area = 5 × 3 = 15

Read Area of Plane Shapes for more information.

Area of Difficult Shapes

To help you understand an area, imagine painting it and how much paint you might use.

You 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

You 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

If you know the coordinates of each corner point you can use the method explained in Area of Irregular Polygons:

There is an Area of a Polygon by Drawing Tool if you need it.

Area by Counting Squares

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

Area Count
This 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)

Sometimes the squares may not match the shape exactly, so you will need to "approximate" an 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 just use your eyes and count a whole square when the areas seem to add up, like with this circle, where the area marked "4" seems equal to about 1 whole square (also for "8"):

Area Count
This circle has an area of approximately 14